VERSITY   OF   ILLINOIS   BULLETIN 


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voi.  XVIII  JANUARY  24,  1921  No.  21 

(Entered  as  second-class  matter  Deceember  11,  1912,  at  the  post  office  at  Urbana,  Illinois,  under  the 
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BUREAU  OF  EDUCATIONAL  RESEARCH— BULLETIN  No.  5 

Report  of  Division  of 
Educational  Tests  for  '19-20 


BY 


WALTER  S.  MONROE 

Assistant  Director 
Bureau  of  Educational  Research,  University  of  Illinois 


PRICE,  25  CENTS 


PUBLISHED  BY  THfe  UNIVERSITY  OF  ILLINOIS 
URBANA,  ILLINOIS 


BUREAU  OF  EDUCATIONAL  RESEARCH— BULLETIN  No.  5 


'  i '  i 


Report  of  Division  of 
Educational  Tests  for  '19-20 


WALTER  S,  MONROE 

Assistant  tiirttfor 

Bureau  of  Educational  Research 
University  of  Illinois 


PRICE,  25  CENTS 


PUBLISHED  BY  THE  UNIVERSITY  OF  ILLINOIS 

URBANA,  ILLINOIS 


.-•-:.    :  .\  '   - 
-.:.:  *:t,.;;*W 


Bulletins  of  the  Bureau  of  Educational  Research 

B.  R.  BUCKINGHAM,  Editor 


464822 


EDITORIAL  INTRODUCTION 

We  should  like  to  have  the  reader  consider  this  monograph  as, 
in  a  certain  sense,  "chips  from  the  work-shop."  We  hold  that  no  orga- 
nization, such  as  that  from  which  this  bulletin  emanates,  should  collect 
from  users  of  test  materials  the  results  which  they  have  attained  in  their 
localities  and  hoard  them  in  miserly  fashion  for  its  own  purposes.  More- 
over, it  is  not  so  nominated  in  the  bond.  It  is  understood  that  when 
copies  of  score  sheets  are  mailed  to  us  we  are  to  combine  them  into  master 
score  sheets  and  to  issue  tabulations  which  will  indicate  over  a  wider 
field  than  any  school  system  affords  the  conditions  disclosed  by  the  tests 
in  question. 

Although  the  Bureau  of  Educational  Research  of  the  University 
of  Illinois  went  out  of  the  business  of  distributing  tests  last  November, 
there  had  been  collected  up  to  that  time  a  valuable  body  of  data  which  was 
augmented  during  the  succeeding  months  until  it  now  appears  to  justify 
publication. 

Aside,  therefore,  from  chapters  three  and  four,  which  deal  with 
Monroe's  Standardized  Reasoning  Test  in  Arithmetic  and  his  Timed 
Sentence  Spelling  Test,  the  bulletin  is  devoted  to  presenting  material 
which  will  make  it  possible  to  use  a  number  of  tests  more  intelligently. 
We  do  not,  as  Dr.  Monroe  says,  attempt  in  this  bulletin  to  give  directions 
for  administering  tests  or  interpreting  results.  We  are  mainly  concerned 
with  what  the  results  are.  We  are  continually  receiving  questions  from 
practical  workers  in  the  field.  These  questions  have  led  us  to  believe 
that  they  are  much  interested  in  and  perplexed  by  the  question  of  standards. 

Realizing  this  fact  we  have  tried  to  make  our  presentation  of  re- 
sults as  complete  and  helpful  as  possible.  They  are  presented  substantially 
in  three  ways.  First,  we  show  for  each  test  the  median  scores  by  grade. 
In  tables  devoted  to  this  sort  of  data  we  also  include  the  25-  and  75-  per- 
centiles.  To  those  who  understand  the  meaning  of  these  latter  figures  the 
nature  of  the  distribution  out  of  which  the  medians  arise  will  be  made 
evident.  If  the  75-  and  25-  percentiles  are  far  apart  it  means  that  the 
data  are  scattering.  In  other  words  that  the  distribution  of  scores  spreads 
over  a  wide  range. 

In  order  that  there  might  be  no  doubt  about  the  nature  of  the 
distribution,  we  have  in  the  second  place  presented  for  each  test,  the 
number  of  pupils  attaining  the  indicated  scores  in  each  grade  to  which 


the  test  was  applied.  The  value  of  this  sort  of  a  showing  is  greater  than 
the  practical  teacher  is  likely  to  realize  upon  the  first  inspection.  Such  a 
table  may  be  converted  into  a  table  indicating  a  distribution  in  terms  of 
percents  by  dividing  each  of  the  entires  by  the  column  totals.  When  the 
table  is  thus  converted  it  becomes  directly  comparable  with  a  similar 
table  which  may  be  computed  for  a  school  or  school  system.  Moreover, 
since  it  is  customary  to  give  the  grade  medians  in  connection  with  this  type 
of  table — and  the  custom  is  followed  in  this  bulletin — the  teacher  may 
learn  from  these  figures  the  number  and  percent  of  pupils  in  each  grade 
exceeding  or  falling  short  of  the  median  of  other  grades.  A  teacher  may 
likewise  discover  from  such  tables  a  number  of  subordinate  facts  concerning 
the  test  and  its  applicability  to  the  grades  in  question — such  facts  as  the 
number  of  zero  scores  or  scores  in  the  neighborhood  of  zero,  the  number  of 
perfect  or  nearly  perfect  scores,  and  the  nature  of  the  distribution  of  the 
frequencies  throughout. 

But  it  is  probable  that  the  greatest  usefulness  of  these  distribution 
tables  is  of  another  sort.  They  are  indispensible  to  those  who  wish  to 
contribute  toward  the  better  standardization  of  tests.  For  example  the 
3000  pupils,  more  or  less,  in  each  grade,  whose  scores  are  shown  in  Table 
II  for  Monroe 's  Reasoning  Test  may  reasonably  be  thought  to  be  insuffi- 
cient for  a  final  standardization.  This  tabulation  provides  a  form  and 
makes  a  beginning  for  a  more  reliable  treatment  of  the  test  in  question. 
Any  superintendent  can  place  the  pupils  whom  he  has  tested — be  they  few 
or  many — in  this  scheme.  Any  bureau  of  research  may  gather  scores 
from  schools  and  school  systems  in  this  manner.  After  a  little  it  may 
(and  indeed  it  should)  publish  its  findings  in  this  manner  to  the  end  that 
more  reliable  standards  may  be  secured.  It  is  because  tables  of  this  sort 
are  costly  to  print  and  of  little  direct  school  use  that  they  are  so  seldom  seen. 
They  are  frequently  found  after  they  have  been  converted  into  percentage 
distributions,  because  the  latter  are  useful  in  making  comparisons.  But 
they  are  seldom  found  in  mere  frequency,  form.  Yet  the  presentation  of 
such  tables  is  fundamental  to  cooperative  effort.  In  our  judgment  every 
research  organization  ought  to  publish  material  in  this  form.  Its  high 
value  for  research  purposes  should  be  appreciated  in  contrast  with  its 
low  value  for  immediate  practical  purposes. 

On  the  other  hand,  the  third  form  of  tabulation  is  of  most  value  for 
school  uses.  We  are  referring  to  the  percentile  tables  presented  in  the 
appendix.  We  are  convinced  that  when  this  type  of  material  is  better 
understood  it  will  be  much  more  widely  used.  By  means  of  it  a  teacher 
may  "place"  a- pupil's  score  among  one  hundred  scores,  arranged  from 
highest  to  lowest,  these  one  hundred  scores  being  regarded  as  typicaL 
Thus  the  percentile  table  will  enable  a  fifth-grade  teacher  to  state  that  a 


pupil  is  (say)  twentieth  among  one  hundred  typical  children  of  his  grade 
in  speed  of  reading,  that  he  is  thirty-seventh  in  the  operations  of  arithmetic, 

fiftieth  in  spelling,  etc.  If  he  is  fiftieth  in  spelling  we  have  the  special 
case  of  the  median,  which  we  ordinarily  arrive  at  from  another  point  of 
view. 

In  using  percentile  tables  such  as  those  given  in  the  appendix  of 
this  bulletin,  regard  must  be  had  for  the  source  of  the  tables.  In  its  ideal 
form  a  percentile  table  is  supposed  to  have  been  derived  from  a  sufficient 
random  sampling  of  a  total  "population" — e.  g.,  from  the  entire  fifth-grade 
in  American  schools,  or  from  the  entire  number  of  ten-year-olds  in  rural 
schools,  or  from  the  entire  number  of  graduates  of  the  Chicago  high  schools. 
In  ranking  a  child's  performance  one  must  be  sure  either  that  he  belongs  to 
the  population  to  which  the  table  refers  or  that  the  population  of  both  the 
child  and  the  table  are  indicated.  Thus  if  a  fifth-grade  pupil  obtains  a 
score  in  composition  equal  to  the  80-percentile  for  his  grade,  we  thereby 
define  his  rank  as  twentieth  from  the  top  (or  eightieth  from  the  bottom) 
among  one  hundred  typical  fifth  grade  children.  A  pupil  thus  ranked 
has  evidently  done  rather  well  compared  with  pupils  of  his  own  grade. 
Very  appropriately  therefore,  we  may  wish  to  rank  him  with  reference  to 
the  sixth  grade.  His  score  may  perhaps  equal  the  60-percentile  of  the 
sixth  grade.  Accordingly,  he  would  be  ranked,  on  his  performance,  as 
fortieth  from  the  top  among  one  hundred  typical  sixth-grade  children. 
Similarly  he  may  rank  as  fiftieth  (median)  for  the  seventh  grade. 

We  submit  these  percentile  tables  for  their  practical  utility.  They 
are,  however,  based  upon  a  limited  number  of  cases;  and  they  will  be 
somewhat  modified  when  more  scores  have  been  made  available. 

From  the  above  statements  it  will  be  clear  that  the  chief  purpose 
of  this  bulletin  is  to  furnish  an  accounting  of  the  test  results  which  we  have 
received.  Nevertheless,  we  have  included  two  chapters  (III  and  IV) 
on  the  derivation  of  Monroe's  reasoning  tests  and  timed  sentence  tests. 
These  accounts  have  been  held  up  a  long  time.  When,  therefore,  they  were 
released,  we  took  account  of  the  demand  that  has  been  made  for  then — 
especially  the  one  relative  to  the  reasoning  test — and  incorporated  them 
into  this  report  of  the  Division  of  Educational  Tests. 


TABLE  OF  CONTENTS 
Chapter  Page 

I.  INTRODUCTION 9 

II.  TENTATIVE  GRADE  NORMS 12 

A.  Monroe's  Standardized  Reasoning   Tests   in   Arithmetic....  12 

B.  Buckingham's  Scale  for  Problems  in  Arithmetic 14 

C.  Monroe's  Diagnostic  Tests  in  Arithmetic 16 

D.  Monroe's  Standardized  Silent  Reading  Tests 19 

E.  Charters '  Diagnostic  Language,  and  Language  and  Grammar 

Tests 25 

F.  Willing 's  Scale  for  Measuring  Written  Composition 26 

G.  Harlan's  Test  for  Information  in  American  History 28 

H.  Sackett's  Scale  in  United  States  History 29 

I.   Hotz's  First  Year  Algebra  Scale 30 

J.   Minnick's  Geometry  Tests 31 

K.  Holley's  Sentence  Vocabulary  Scale 32 

L.  Holley's  Picture  Completion  Test  for  Primary  Grades 34 

III.  THE  DERIVATION  OF  MONROE'S  STANDARDIZED  REASONING  TESTS  IN 

ARITHMETIC 36 

IV.  MONROE  's  TIMED  SENTENCE  SPELLING  TESTS  AND  PUPILS  '  ERRORS.    48 
APPENDIX:    PERCENTILE  SCORES 57 

1.  Monroe's  Standardized  Reasoning  Tests  in  Arithmetic. 

2.  Monroe's  Standardized  Silent  Reading  Tests. 

3.  Charters'  Diagnostic  Language  Tests  for  Grades  III  to  VIII. 

A.  Pronouns 

B.  Verbs 

C.  Miscellaneous  A 

D.  Miscellaneous  B 

4.  Charters'   Diagnostic   Language  and    Grammar  Tests  for 

Grades  VII  to  VIII 

A.  Pronouns 

B.  Verbs 

C.  Miscellaneous 

5.  Willing 's  Scale  for  Measuring  Written  Composition 

6.  Harlan  's  Test  for  Information  in  American  History. 

7.  Hotz's  First  Year  Algebra  Scale 

8.  Holley's  Sentence  Vocabulary  Scale. 

8 


CHAPTER  I 

INTRODUCTION 

Source  of  data.  In  distributing  educational  tests  the  Bureau  of  Edu- 
cational Research  has  always  supplied  a  duplicate  class  record  sheet  on  which 
was  printed  a  request  that  the  duplicate  be  returned  after  the  scores  had  been 
entered  upon  it.  There  has  been  no  effort  to  follow  up  the  purchasers  of  the 
tests  in  order  to  secure  complete  returns  of  the  scores.  Consequently,  this 
report  is  based  upon  the  scores  voluntarily  contributed.  The  bulk  of  the  scores 
are  from  medium  sized  cities.  Reports  have  been  received  from  a  few  large 
cities  (population  of  100,000  or  more)  for  Monroe 's  Standardized  Silent  Read- 
ing Tests  but  in  no  other  case  has  more  than  one  such  city  reported.  Practically 
no  scores  were  reported  from  rural  schools  except  for  Monroe's  Standardized 
Silent  Reading  Tests.  Several  tests  distributed  by  the  Bureau  of  Educational 
Research  are  not  included  in  this  report  for  the  reason  that  the  number  of  scores 
reported  seemed  to  be  too  small  to  justify  any  announcement  of  median 
scores  which  would  be  useful  as  tentative  standards. 

Form  of  the  report.  The  distributions  of  scores  entered  upon  the  class 
record  sheets  were  combined  to  form  a  total  distribution  of  scores  for  each 
yearly  grade.  No  attempt  was  made  to  keep  separate  the  scores  of  the  A  and 
B  sections  of  the  yearly  grades.  In  addition  to  the  median  scores  for  each 
grade  the  25-  and  75-  percentile  scores  are  also  given  for  several  of  the  tests. 
In  a  few  cases  the  total  distributions  are  given  because  they  have  a  special 
significance.  In  the  Appendix  of  this  bulletin  the  5-,  10-,  20-,  30-,  40-,  50-, 
60-,  70-,  80-,  90-,  and  95-  percentile  scores  are  given  for  a  number  of  the  tests. 
The  publication  of  the  percentile  scores  is  prompted  by  the  desire  to  make 
possible  a  more  accurate  interpretation  of  a  pupil 's  score  than  merely  that  it  is 
above  or  below  the  median  score.  Pupils  belonging  to  any  grade  exhibit  large 
individual  differences.  For  this  reason  it  is  frequently  desirable  to  know  where 
the  score  of  a  pupil  places  him  in  the  total  distribution  from  which  the  median 
for  his  grade  was  calculated.  The  percentile  scores  make  it  possible  to  ascer- 
tain, for  any  pupil  his  approximate  position  in  this  total  distribution.  For 
example,  if  a  pupil 's  score  is  equal  or  superior  to  the  80-  percentile  score  for 
his  grade,  he  ranks  in  the  upper  20  percent  of  all  pupils  to  whom  the  test  was 
given  in  that  grade. 

Time  of  testing.  No  attempt  was  made  to  organize  the  giving  of  the 
tests.  Consequently,  the  scores  on  which  the  median  and  percentile  scores  are 
based  represent  testings  all  the  way  from  September  to  June.  This  condition 
makes  the  derived  scores  somewhat  less  useful  as  tentative  grade  standards  than 
they  would  be  if  they  were  based  upon  measures  obtained  at  some  one  fixed 


10 

time  during  the  school  year.  The  situation  is  further  complicated  by  reason 
of  the  fact  that  some  of  the  schools  reporting  have  semi-annual  promotion  while 
others  have  annual  promotion.  Some  of  those  which  have  semi-annual  pro- 
motion combined  the  A  and  B  divisions  of  each  grade  in  making  their  reports. 
In  order  that  the  median  and  percentile  scores  shall  have  as  definite  a  meaning 
as  possible  we  have  estimated  for  each  test  the  month  of  the  school  year  which 
the  median  scores  appear  to  represent.  This  estimate,  however,  must  be  con- 
sidered only  approximate. 

An  organized,  cooperative  plan  which  would  have  resulted  in  the  tests 
being  given  on  one  or  more  fixed  dates  during  the  school  year,  was  not  attempted 
for  two  reasons.  In  the  first  place,  the  complete  realization  of  such  a  plan  was 
impossible  because  in  a  large  number  of  school  systems  the  tests  were  given  as 
a  part  of  a  local  plan.  The  Bureau  of  Educational  Research  believes  it  is  wise 
to  encourage  this  use  of  educational  tests.  When  the  tests  are  given  merely 
as  a  part  of  a  project  originated  by  a  central  bureau  of  research,  little  use  is 
likely  to  be  made  of  the  results  by  the  schools  giving  them.  Their  motive  is 
to  cooperate  with  the  central  bureau,  and  when  this  has  been  completed  there 
is  a  tendency  for  them  to  feel  that  all  has  been  accomplished  which  may  be 
accomplished.  This  results  in  a  great  waste.  Information  which  might  be  of 
much  value  to  the  local  school  systems  is  not  used.  Furthermore,  this  practise 
tends  to  engender  an  attitude  toward  educational  tests  that  they  are  merely 
tools  of  research  to  be  used  by  central  research  bureaus  and  not  tools  which  may 
be  used  by  a  school  system,  or  even  a  teacher,  in  improving  instruction. 

A  second  reason  for  not  attempting  to  organize  the  giving  of  the  tests  was 
that  tests  were  distributed  in  all  sections  of  the  United  States  and  in  a  few 
foreign  countries.  It  would  have  been  impossible  to  solicit  the  cooperation  of 
all  who  gave  the  tests  in  a  plan  of  organized  testing. 

The  interpretation  of  scores  by  comparison  with  grade  norms. 
It  is  not  the  purpose  of  this  bulletin  to  give  detailed  suggestions  concerning  the 
use  of  the  grade  medians  and  percentile  scores  in  the  interpretation  of  the  scores 
obtained  in  any  school  system  by  giving  the  tests.  In  another  place1  the  writer 
has  indicated  in  some  detail  the  general  procedure  to  be  followed  in  interpreting 
scores  for  the  purpose  of  improving  instruction.  Grade  norms  are  also  useful 
in  interpreting  the  scores  of  pupils  for  the  purpose  of  classification.2 

In  any  interpretation  of  scores,  either  individual  or  group,  it  is  necessary 
to  bear  in  mind  certain  limitations.  In  the  first  place  none  of  our  educational 
tests  yield  scores  which  are  absolutely  accurate.  The  errors  of  measurement 
are  large  Ln  comparison  with  the  errors  made  in  the  measurement  of  physical 
objects.  Errors  larger  than  the  difference  between  the  median  scores  for  suc- 


lMonroe,  Walter  S.  "Improvement  of  Instruction  Through  the  use  of  Educational 
Tests,"  Journal  of  Educational  Research,  I  (February,  1920),  96-102. 

Buckingham,  B.R.  "Suggestions  for  procedure  following  a  testing  program — I, 
Reclassification,"  Journal  of  Educational  Research,  II  (December,  1920),  787-801. 


11 

cessive  school  grades  frequently  occur  although  in  the  case  of  our  better  tests 
the  majority  of  the  errors  are  less.  These  errors  of  measurement  are  chance 
•errors  and  for  that  reason  tend  to  neutralize  each  other  in  the  median  and  average 
scores  of  groups.  Therefore,  the  group  scores  are  more  accurate  than  individual 
scores.  However,  in  interpreting  either  type  of  scores  one  should  bear  in  mind 
the  possible  errors  of  measurement  which  they  may  include. 

In  the  second  place  the  score  which  a  pupil  makes  on  any  subject- 
matter  test,  such  as  reading,  arithmetic,  history,  or  language,  depends  in  part 
upon  his  general  intelligence.  Pupils  belonging  to  any  school  grade  differ  widely 
with  respect  to  their  general  intelligence  and  consequently  may  be  expected  to 
differ  in  their  achievements.  For  this  reason  some  pupils  belonging  to  a  given 
grade  should  have  scores  above  the  median,  while  others  may  be  expected  to 
have  scores  below  the  median  because  of  their  differences  in  capacity  to  learn. 
There  are  also  differences  in  the  average  general  intelligence  of  pupils  belonging 
to  the  same  school  grade.  For  example,  the  average  general  intelligence  of  the 
fifth-grade  pupils  in  one  school  may  be  a  year  or  more  above  that  of  the  fifth- 
grade  pupils  in  another  school.  It  is  unfair  to  both  pupils  and  teachers  to 
interpret  achievement  scores  without  recognizing  the  differences  which  may  exist 
in  the  general  intelligence  of  the  pupils.  To  do  so  will  frequently  result  in 
arriving  at  erroneous  conclusions.  Hence,  grade  standards  such  as  are  given 
in  this  report  must  be  used  with  due  caution. 

Chapters  III  and  IV  contain  reports  of  studies  which  were  made  by  the 
writer  during  the  time  he  was  Director  of  the  Bureau  of  Educational  Measure- 
ments and  Standards  of  the  Kansas  State  Normal  School,  Emporia,  Kansas. 
These  reports  were  originally  prepared  for  publication  by  that  institution. 
Permission  has  been  obtained  to  incorporate  them  in  this  bulletin.  In  doing 
this  the  manuscript  has  been  only  slightly  revised.  Chapter  III  gives  an  ac- 
count of  the  derivation  of  the  Monroe  Standardized  Reasoning  Tests  in  Arith- 
metic. Chapter  IV  contains  a  description  of  the  derivation  of  Monroe 's  Timed 
Sentence  Spelling  Tests  and  a  report  of  a  study  of  pupils'  errors  in  spelling 
based  upon  them. 


CHAPTER  II 

TENTATIVE  GRADE  NORMS 

The  percentile  scores  as  well  as  the  median  scores  which  are  given  in 
this  chapter  should  be  used  only  as  tentative  grade  standards.  For  several 
of  the  tests  the  number  of  scores  on  which  these  are  based  is  so  small  that  the 
standards  can  not  be  thought  of  as  final.  When  other  scores  are  added  to  the 
distributions,  it  is  likely  that  different  medians  will  be  obtained.  Furthermore, 
such  standards  should  always  be  thought  of  as  representing  the  average  of 
present  conditions  and  not  as  being  ideal  standards  or  what  ought  to  be. 

A.     MONROE'S     STANDARDIZED    REASONING  TESTS  IN  ARITHMETIC 

The  derivation  of  these  tests,  which  consist  of  a  series  of  one-  and  two- 
step  problems,  is  described  in  Chapter  III.  For  each  problem  two  values  were 
calculated,  "correct  principle  value,"  or  P,  and  "correct  answer, value,"  or  C. 
These  values  represent  the  credit  which  is  to  be  given  for  solving  the  problem 
correctly  in  principle  and  for  obtaining  the  correct  answer.  Each  problem 
is  marked  for  correct  principle.  If  a  problem  is  solved  correctly  in  principle 
it  is  further  marked  with  reference  to  correct  answer.  A  pupil  does  not  receive 
credit  for  a  correct  answer  if  the  problem  was  solved  by  the  wrong  principle. 
The  directions  for  administering  the  tests  provide  for  having  the  pupils  mark 
the  problem  on  which  they  are  working  at  the  end  of  ten  minutes.  In  this  way 


TABLE  I. 


MONROE'S  STANDARDIZED  REASONING  TESTS  IN  ARITHMETIC. 
FORM  I.    GRADE  NORMS  FOR  APRIL  TESTING 


GRADE 

IV 

V 

VI 

VII 

VIII 

CORRECT  PRINCIPLE 

Number  of  pupils. 

2932 

3027 

3498 

2796 

2472 

25-percentile 

6.2 

12.1 

10.0 

13.8 

11.5 

Median 

11.3 

19.2 

14.2 

19.7 

17.2 

75-percentile 

16.8 

25.9 

19.4 

24.7 

22.8 

*RATE 

Number  of  pupils 

1412 

1705 

1699 

1717 

1642 

25-percentile 

5.2 

8.0 

6.4 

8.0 

5.3 

Median 

7.8 

11.2 

8.7 

11.2 

7.5 

75-percentile 

8.1 

15.1 

12.1 

14.5 

10.9 

CORRECT  ANSWERS 

Number  of  pupils 

2968 

2996 

3518 

2803 

2515 

25-percentile 
Median 

4.1 
7.0 

7.1 
11.3 

6.9 
10.4 

9.4 

13.4 

5.1 
9.0 

75-percentile 

10.7 

15.5 

14.0 

17.4 

13.0 

*Sum  of  correct  principle  values  of  problems  done  correctly  within  ten  minutes. 


13 


a  rate  score  may  be  obtained.  It  is  the  sum  of  the  "principle  values"  of  the 
problems  which  are  solved  correctly  in  principle  within  ten  minutes.  However, 
the  obtaining  of  the  rate  score  is  optional,  and  it  was  reported  in  only  about 
half  of  the  cases. 

There  are  two  forms  of  these  tests.  These  forms  were  constructed  so 
that  they  were  expected  to  be  equivalent.  Experience  in  using  them  suggests 
that  they  are  not  equivalent,  although  data  are  lacking  at  this  time  on  which 
a  statement  concerning  their  comparability  may  be  based.  No  scores  are 
reported  for  Form  2  because  the  returns  received  for  this  form  included  an 
insufficient  number  of  cases. 

Test  I  is  given  in  Grades  IV  and  V,  Test  II  in  Grades  VI  and  VII,  and 
Test  III  in  Grade  VIII.  The  tests  were  not  constructed  so  that  the  scores 
yielded  by  the  different  tests  are  comparable.  Therefore,  direct  comparisons 
can  not  be  made  between  the  fourth  and  fifth  grade  scores  and  between  the 
seventh  and  eighth  grade  scores. 

TABLE  II.    MONROE'S  STANDARDIZED 
REASONING  TESTS  IN  ARITHMETIC 
FORM  I,  CORRECT  PRINCIPLE 


GRADE 

SCORE* 

IV 

V 

VI 

VII 

VIII 

43 

3 

11 

41 

5 

39 

7 

20 

37 

1 

21 

35 

12 

89 

33 

11 

56 

31 

26 

137 

56 

29 

25 

120 

47 

127 

94 

27 

40 

191 

93 

262 

63 

25 

80 

191 

131 

202 

171 

23 

89 

223 

135 

242 

214 

21 

124 

269 

248 

304 

233 

19 

130 

207 

280 

322 

214 

17 

161 

211 

306 

259 

217 

15 

248 

231 

328 

225 

237 

13 

260 

219 

470 

225 

203 

11 

298 

167 

425 

193 

201 

9 

267 

166 

374 

134 

133 

7 

294 

148 

276 

103 

154 

5 

304 

140 

191 

52 

121 

3 

230 

94 

123 

30 

87 

I 

185 

54 

49 

18 

51 

0 

137 

57 

22 

8 

23 

Total 

2932 

3027 

3498 

2706 

2472 

Median 

11.3 

19.2 

14.2 

19.7 

17.2 

*  In  this  bulletin  all  intervals  unless  other- 
wise noted  are  expressed  in  terms  of  their 
lower  limits. 


14 

Table  I  gives  the  grade  medians,  25-percentile,  and  75-percentile  scores 
for  correct  principle,  correct  answer,  and  rate.  The  distributions  of  scores  for 
correct  principle  are  given  in  Table  II.  These  indicate  that  Test  I  is  too 
difficult  for  a  number  of  pupils  in  the  fourth  and  fifth  grades.  In  the  construc- 
tion of  the  tests  no  effort  was  made  to  include  very  easy  problems.  In  fact, 
as  is  shown  in  Chapter  III,  the  difficulty  of  a  problem  was  not  considered  as 
a  basis  for  selection.  In  none  of  the  other  grades  do  the  zero  scores  amount  to 
as  much  as  one  per  cent  of  the  total.  In  the  seventh  grade  nearly  five  percent 
of  the  pupils  made  perfect  scores. 

REFERENCES 

Willing,  M.  H.  "The  Encouragement  of  Individual  Instruction  by  Means  of  Standard- 
ized Tests,"  Journal  of  Educational  Research,  I  (March,  1920),  193-198. 

Results  from  the  Monroe  Scandardized  Reasoning  Tests  are  used  to  illustrate  how  such 
work  as  the  title  mentions  may  be  carried  on.  Suggestions  for  diagnosis  of  faults,  remedial 
measures,  etc.  are  given. 

B.     BUCKINGHAM'S    SCALE    FOR    PROBLEMS    IN    ARITHMETIC. 

The  problems  for  Buckingham 's  scale  were  selected  largely  on  the  basis 
of  difficulty.  Division  One  is  for  Grades  III  and  IV,  Division  Two  for  Grades 
V  and  VI,  and  Division  Three  for  Grades  VII  and  VIII.  The  problems  of 
Division  One  increase  by  steps  of  approximately  0.3  P.  E.  from  2.7  to  5.3. 
The  problems  of  Division  Two  increase  by  similar  steps  of  difficulty  from  5.5 
to  7.3,  and  the  problems  of  Division  Three  increase  from  7.5  to  9.4.  In  scoring 
the  test  papers  attention  is  given  only  to  the  numerical  accuracy  of  the  answers. 
A  pupil 's  score  is  the  difficulty  value  of  the  hardest  problem  which  he  answers 
correctly,  unless  he  has  failed  on  one  or  more  previous  problems.  In  that  case, 
a  correction  is  made  by  subtracting  from  the  value  of  the  hardest  correctly 
solved  problem  0.3  for  each  failure  in  Division  One,  or  0.2  for  each  failure  in 
Division  Two  or  Three.  Thus,  if  a  pupil  solved  the  first  six  problems  in  Divi- 
sion One,  his  score  is  4.2;  but  if  he  fails  on  the  4th  and  5th  (otherwise  succeeding 
through  the  6th),  his  score  is  3.6 — i.e.,  4.2  — 2  x  0.3. 


TABLE  III.    BUCKINGHAM 'S  SCALE  FOR  PROBLEMS  IN  ARITHMETIC. 
I.    GRADE  NORMS  FOR  JUNE  TESTING. 


FORM 


GRADE 

III 

IV 

V 

VI 

VII 

VIII 

No.  of  pupils 
25-Percentile 
Median 
75-Percentile 

4181 
3.4 
3.8 
4.3 

4589 
4.2 
4.6 

5.2 

7142 
5.7 
5.9 
6.3 

5927 
5.9 
6.4 
6.8 

6632 
7.6 
7.8 

8.3 

5269 
7.7 
8.2 
8.7 

Although  the  three  divisions  of  the  scale  were  constructed  so  that  it  was 
expected  that  the  scores  obtained  from  the  different  divisions  would  be  com- 


15 

parable,  the  grade  medians  given  in  Table  III  clearly  indicate  that  the  scores 
are  not  comparable.  The  increase  in  the  median  scores  from  the  third  grade 
to  the  fourth  grade  is  0.8.  The  increase  from  the  fourth  grade  to  the  fifth  grade 
is  1.3.  A  similar  variation  is  found  in  the  differences  between  the  subsequent 
grades.  Therefore,  the  scores  obtained  by  the  different  divisions  of  the  scale 
are  not  comparable.  The  reason  for  this  is  that  the  pupils  taking  Division  Two 
or  Division  Three  do  not  have  an  opportunity  to  do  the  problems  of  the  lower 
divisions.  If  they  did,  a  number  of  them  would  fail  to  do  all  of  them  correctly. 
Thus,  they  would  receive  a  score  lower  than  that  which  they  receive  when 
taking  only  the  higher  divisions. 


TABLE     IV.    BUCKINGHAM'S     SCALE     FOR 

PROBLEMS  IN  ARITHMETIC.     FORM  I 

GRADE    DISTRIBUTIONS    FOR 

JUNE  TESTING 


GRADE 

SCORE 

III 

IV 

V 

VI 

VII 

VIII 

9.0 

328 

699 

8.5 

6 

782 

1084 

8.0 

1 

4 

11 

1349 

1290 

7.5 

14 

13 

2931 

1740 

7.0 

240 

775 

58 

44 

6.5 

2 

1012 

1886 

6.0 

6 

1540 

1504 

5.5 

2 

21 

3663 

1569 

5.0 

131 

1069 

106 

57 

4.5 

490 

1474 

14 

12 

4.0 

815 

863 

3.5 

1305 

798 

3.0 

967 

255 

2.5 

298 

75 

0 

173 

25 

549 

94 

1184 

412 

Total 

4181 

4589 

7142 

5927 

6632 

5269 

Median 

3.8 

4.6 

5.9 

6.4 

7.8 

8.2 

In  Table  IV  the  total  distributions  are  given.  Evidently  a  division  of 
the  scale  higher  or  lower  than  that  designed  for  the  grade  has  been  used  in  a 
few  cases.  The  distributions  are  significant  in  that  they  show  that  the  divi- 
sions of  the  scale  are  too  difficult  for  the  respective  grades.  The  percent  of 
pupils  making  zero  scores  in  the  third,  fifth,  seventh,  and  eighth  grades  is  so 
large  that  the  scale  as  now  published  must  be  considered  unsatisfactory  for 
these  grades.  This  condition  could  be  remedied  in  the  case  of  Division  Two 
and  Division  Three  by  giving  the  next  lower  division  to  the  pupils  who  make 
zero  scores.  In  the  case  of  Division  One,  the  scale  will  have  to  be  extended 
downward  by  adding  less  difficult  problems. 


16 

REFERENCES 

First  Annual  Report,  Bureau  of  Educational  Research,  University  of  Illinois,  pp.  21-22. 
These  pages  contain  a  very  brief  suggestion  of  what  was  done  along  the  line  of  this  scale 
that  seemed  to  justify  its  construction,  also  a  short  description  of  the  scale. 

Buckingham,  B.R.  "Notes  on  the  Derivation  of  Scales  in  School  Subjects,  with  Special 
Application  to  Arithmetic,"  Fifteenth  Yearbook  of  National  Society  for  the  Study  of 
Education,  Part  I,  pp.  23-40. 

This  presents  a  report  of  a  series  of  problems  which  was  given  to  a  number  of  school  children 
in  New  York  and  other  cities.  The  results  are  given  and  discussed,  especially  with  reference 
to  locating  the  problems  on  a  scale.  Although  this  scale  is  not  the  one  now  in  use,  it  is 
similar  to  it. 

C.     MONROE'S  DIAGNOSTIC  TESTS  IN  ARITHMETIC. 

Monroe 's  Diagnostic  Tests  in  Arithmetic  consist  of  four  parts.  Part  I 
includes  Tests  1  to  6.  Part  II  includes  Tests  7  to  1 1.  These  tests  involve  only 
integers.  Part  III  includes  Tests  12  to  16,  which  consist  of  examples  involving 
common  fractions.  Part  IV  includes  Tests  17  to  21,  which  consist  of  examples 
involving  multiplication  and  division  of  decimal  fractions.  Tables  V  and  VI 


TABLE    V.    MONROE'S    DIAGNOSTIC    TESTS    IN    ARITHMETIC. 
MEDIANS    FOR    APRIL    TESTING.     RATE  (NUMBER 
OF  EXAMPLES  ATTEMPTED) 


GRADE 


GRADE 

IV 

V 

VI 

VII 

VIII 

PART  I 

(Approximate  number  of  pupils) 

900 

480 

590 

600 

600 

Test  1 

7.2 

11.6 

13.3 

12.6 

14.0 

Test  2 

4.1 

7.2 

9.3 

8.6 

9.2 

Test  3 

3.3 

5.0 

5.8 

5.7 

7.2 

Test  4 

2.0 

3.2 

4.0 

4.7 

5.7 

TestS 

3.9 

4.8 

5.6 

5.7 

6.2 

Test  6 

1.7 

2.7 

3.1 

3.0 

4.0 

PART  II 

(Approximate  number  of  pupils) 
Test  7 

380 
3.8 

760 

4.2 

610 

5.5 

520 
5.3 

460 
6.3 

Test  8 

3.0 

4.1 

5.5 

6.1 

6.6 

Test  9 

4.8 

5.9 

8.2 

8.6 

9.8 

Test  10 

2.8 

3.2 

5.3 

5.3 

6.7 

Test  11 

1.6 

2.2 

2.2 

2.9 

3.7 

PART  III 

(Approximate  number  of  pupils) 
Test  12 

370 
5.8 

1000 
7.6 

580 
8.6 

560 
9.4 

Test  13 

4.5 

5.4 

6.0 

6.0 

Test  14 

5.2 

7.1 

8.1 

8.7 

Test  15 

6.2 

7.1 

7.7 

8.1 

Test  16 

5.7 

7.4 

8.0 

9.1 

PART  IV 

(Approximate  number  of  pupils) 

440 

900 

660 

Test  17 

3.6 

3.5 

4.5 

Test  18 

11.9 

11.5 

12.9 

Test  19 

5.8 

4.5 

5.3 

Test  20 

12.5 

11.1 

13.5 

Test  21 

5.1 

4.3 

4.8 

17 

give  the  median  scores  for  these  tests  in  terms  of  rate  (number  of  examples 
attempted)  and  accuracy  (percent  of  examples  done  correctly).  In  order  to 
simplify  the  administration  of  these  tests  the  plan  of  scoring  has  been  changed 
so  that  the  pupil  is  now  given  only  one  score,  the  number  of  examples  right. 
In  Table  VII  tentative  grade  norms  are  given  in  terms  of  this  score. 

In  the  interest  of  economy,  both  of  cost  of  the  tests  and  time  required 
for  their  administration,  most  of  the  tests  of  this  series  were  made  so  short  that 
there  is  a  lack  of  discrimination  between  pupils.  For  example,  the  increase 
in  the  number  of  examples  attempted  from  grade  to  grade  is  frequently  less  than 
one  example.  The  shortness  of  th^  tests  also  makes  the  errors  of  measurement 
relatively  large. 

This  group  of  tests  was  designed  for  diagnostic  purposes,  i.  e.,  it  was  in- 
tended to  measure  separately  the  abilities  of  pupils  to  do  the  important  types  of 


TABLE  VI.    MONROE'S  DIAGNOSTIC  TESTS  IN  ARITHMETIC.    GRADE 

MEDIANS  FOR  APRIL  TESTING.    ACCURACY  (PERCENT 

OF  EXAMPLES  CORRECT) 


GRADE 

IV 

V 

VI 

VII 

VIII 

PART  I 

Approximate  number  of  pupils 

900 

480 

590 

600 

600 

Testl 

100 

100 

100 

100 

100 

Test  2 

66.6 

86.8 

100 

100 

100 

Test  3 

56.5 

72.3 

80.8 

82.0 

87.6 

Test  4 

28.0 

55.1 

71.9 

79.8 

85.4 

TestS 

52.5 

61.7 

66.9 

67.9 

75.1 

Test  6 

22.4 

49.5 

64.0 

77.5 

100 

PART  II 

Approximate  number  of  pupils 

380 

760 

610 

520 

460 

Test? 

63.2 

65.1 

75.9 

76.3 

81.6 

TestS 

30.4 

52.9 

66.9 

79.8 

78.5 

Test  9 

75.0 

86.3 

91.2 

93.1 

100 

Test  10 

35.2 

58.4 

72.1 

72.3 

81.9 

Test  11 

22.4 

35.5 

53.4 

65.0 

68.2 

PART  III 

Approximate  number  of  pupils 

370 

1000 

580 

560 

Test  12 

35.5 

32.0 

33.6 

49.0 

Test  13 

38.0 

29.2 

36.0 

53.9 

Test  14 

57.5 

70.3 

79.6 

86.0 

Test  15 

37.5 

30.0 

33.6 

45.5 

Test  16 

38.5 

36.8 

59.1 

70.2 

PART  IV 

Approximate  number  of  pupils 

440 

900 

660 

Test  17 

37.6 

36.4 

53.2 

Test  18 

100 

100 

100 

Test  19 

39.6 

47.0 

61.7 

Test  20 

100 

100 

100 

Test  21 

35.6 

44.0 

51.3 

18 

examples  in  the  field  of  the  operations  of  arithmetic.  A  weighted  sum  of  a 
pupil 's  scores  on  such  a  group  of  tests  would  yield  a  general  measure  of  his 
ability  in  this  field.3 


TABLE  VII.    MONROE'S  DIAGNOSTIC  TESTS  IN  ARITHMETIC.    GRADE 
MEDIANS  FOR  APRIL  TESTING.    NUMBER  OF  EXAMPLES  CORRECT 


GRADE 

IV 

V 

VI 

VII 

VIII 

PART! 

Approximate  number  of  pupils 

900 

480 

590 

600 

600 

Test  1 

7.2 

11.6 

13.3 

12.6 

14.0 

Test  2 

2.8 

6.2 

9.3 

8.6 

9.2 

Test  3 

1.9 

3.6 

4.7 

4.7 

6.4 

Test  4 

.6 

1.7 

2.9 

3.6 

4.8 

TestS 

2.0 

3.0 

3.7 

3.8 

4.4 

Test  6 

.4 

1.3 

2.0 

2.3 

4.0 

PART  II 

Approximate  number  of  pupils 

380 

760 

610 

520 

460 

Test? 

2.4 

2.7 

4.2 

4.0 

5.1 

TestS 

.9 

2.2 

3.7 

4.8 

5.2 

Test  9 

3.6 

5.1 

7.5 

8.0 

9.8 

Test  10 

1.0 

1.8 

3.8 

3.8 

5.5 

Test  11 

.4 

.8 

1.2 

1.8 

2.4 

PART  III 

Approximate  number  of  pupils 

370 

1000 

580 

560 

Test  12 

2.0 

2.4 

2.9 

4.6 

Test  13 

1.7 

1.6 

2.2 

3.2 

Test  14 

3.0 

5.0 

6.5 

7.4 

Test  15 

2.3 

2.1 

2.6 

3.7 

Test  16 

2.2 

2.7 

4.7 

6.4 

PART  IV 

Approximate  number  of  pupils 

440 

900 

660 

Test  17 

1.4 

1.3 

2.4 

Test  18 

11.9 

11.5 

12.9 

Test  19 

2.4 

2.1 

3.3 

Test  20 

12.5 

11.1 

13.5 

Test  21 

1.8 

1.9 

2.5 

REFERENCES 

Finley,  G.  W.,    A  Comparative  Study  of  Three  Diagnostic  Arithmetic  Tests.     Colorado 
State  Teachers  College  Bulletin,  Series  XX,  No.  4. 

This  reports  a  study  made  of  the  Cleveland  Survey  Tests,  The  Woody  Arithmetic  Scales  and 
Monroe's  Diagnostic  Tests  in  Arithmetic.  The  tests  were  given  on  six  successive  days  to 
some  60  eighth  grade  pupils.  The  scores  made  are  given  in  detail,  compared  with  each  other 
and  with  scores  obtained  elsewhere. 

Monroe,  W.  S.,     "A  Series  of  Diagnostic  Tests  in  Arithmetic,"     Elementary  School 
Journal,  XIX,  (April,  1919),  585-607. 

This  article  discusses  the  types  of  examples  in  the  four  fundamental  operations,  the  question 
of  "one  dimensional"  vs.  "two  dimensional"  tests,  and  thus  establishes  the  theoretical  bases 
of  the  tests  presented.  The  series  is  described,  a  distribution  of  scores  made  thereon  is  ana- 
lyzed, and  the  value  of  using  such  tests  pointed  out. 

'See  the  group  of  tests  on  the  operations  of  arithmetic  included  in  the  Illinois  Examination. 


19 

Uhl,  W.  L.,     "The  Use  of  Standardized  Materials  in  Arithmetic  for  Diagnosing  Pupils' 
Methods  of  Work,"    Elementary  School  Journal,  XVIII,  (November,  1917),  215-218. 
This  article  contains  no  reference  to  the  Monroe  Tests,  but  describes  an  experiment  in  diag- 
nosis, similar  to  that  made  possible  by  their  use.     Both  finding  specific  faults  and  remedying 
them  is  considered  briefly. 

D.     MONROE'S  STANDARDIZED  SILENT  READING  TESTS. 

Monroe 's  Standardized  Silent  Reading  Tests  have  been  used  so  widely 
that  a  detailed  description  here  is  unnecessary.  Each  test  consists  of  several 
exercises,  each  of  which  has  been  assigned  a  rate  value  and  a  comprehension 
value.  The  rate  value  is  based  upon  the  number  of  words  in  the  exercise  and 
the  comprehension  value  is  based  upon  the  rate  and  accuracy  with  which  pupils 
were  found  to  be  able  to  do  the  exercise.  Test  I  is  for  Grades  III,  IV,  and  V, 
Test  II  is  for  Grades  VI,  VII,  and  VIII,  and  Test  III  is  for  the  high  school. 
There  are  three  forms  of  Tests  I  and  II.  There  are  only  two  forms  of  Test  III. 

The  different  forms  of  these  tests  were  constructed  so  that  they  were 
expected  to  be  equivalent.  The  use  of  the  forms,  however,  indicates  that  they 
are  not  equivalent.  In  order  to  study  the  degree  of  equivalence  of  the  three 
forms,  copies  of  the  different  forms  were  arranged  in  alternate  order  before  the 
test  papers  were  distributed  to  the  pupils.  This  plan  results  in  the  first, 
fourth,  seventh,  tenth,  etc.  pupil  having  a  copy  of  Form  1.  The  second, 
fifth,  eighth,  eleventh,  etc.  pupil  would  have  a  copy  of  Form  2.  The  third, 
sixth,  ninth,  twelfth,  etc.  pupil  would  have  a  copy  of  Form  3.  By  this  plan 
each  form  of  the  test  is  given  to  similar  samples  of  the  school  population. 

Test  I  was  given  to  approximately  775  pupils  and  Test  II  was  given  to 
approximately  645.  The  numbers  of  pupils  taking  the  different  forms  in  each 
grade  differed  slightly.  This  is  an  accidental  result  of  the  way  in  which  the 
test  papers  were  arranged.  The  average  and  the  standard  deviation  have  been 
calculated  for  each  distribution  of  scores.  In  general  the  pupils  made  higher 
scores  on  Forms  2  and  3  than  they  did  on  Form  1.  The  standard  deviations 
are  also  unequal.  This  suggests  that  the  exercises  of  the  different  forms  of 
the  tests  make  somewhat  irregular  scales. 

The  formula  for  reducing  the  scores  obtained  from  one  scale  to  equivalent 
scores  on  another  scale  is  as  follows: 

S,  =-^-82+    (AVI-     ^-A 

(To  0*2 

In  this  formula  S!  is  the  equivalent  score  in  Form  1  and  S2  the  obtained  sorec  in 
Form  2.  Avt  refers  to  the  average  of  the  scores  obtained  from  Form  1,  Av2 
refers  to  the  average  of  the  scores  obtained  from  Form  2.  <r\  is  the  standard 
deviation  of  the  distribution  of  the  Form  1  scores  and  <«  is  the  standard  devia- 
tion of  the  distribution  of  the  Form  2  scores.  This  formula  is  based  upon  the 
usual  assumption  that  the  deviations  from  the  average  are  equal  when  expressed 
in  terms  of  the  standard  deviation  of  the  distribution;  in  other  words  that 


20 


S,  -   AVl         Sj   -  Avs 


When  this  equation  is  solved  for  $!  we  obtain  the  formula  as  given  above. 
Since  the  scores  on  Form  1  are  in  general  smaller  than  the  scores  on  the  other 
two  forms  it  was  decided  to  reduce  both  the  Form  2  and  the  Form  3  scores  to 
the  equivalence  of  Form  1  scores.  The  application  of  the  above  formula 

involves  the  determination  of  the  numerical  value  of  the  ratio  of  —  by  which 

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equivalent  of  the  constant  terms  of  the  formula,  (i.e.,  of  the  expression  in 
parentheses).  This  latter  numerical  equivalent  maybe  plus  or  minus.  When 
it  is  positive  it  is  to  be  added  and  when  negative  it  is  to  be  subtracted. 


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21 

In  Table  VIII,  the  number  of  pupils,  the  average  score  and  the  standard 
deviation  is  given  for  each  form  of  each  test.  In  the  last  two  columns  the 
multiplier  and  the  constant  term  in  the  above  formula  are  given  for  Form  2 
and  Form  3.  These  can  be  used  in  reducing  scores  obtained  from  Form  2  or 
Form  3  to  the  basis  of  Form  1.  In  securing.data  for  these  determinations,  each 
test  was  given  in  each  of  the  three  grades  for  which  it  is  intended.  Except 
in  the  eighth  grade  the  number  of  pupils  in  the  different  grades  was  approxi- 
mately the  same.  The  correction  numbers  were  calculated  for  each  grade 
separately.  Since  they  were  found  to  be  approximately  the  same  it  was  decided 
to  combine  the  scores  from  the  different  grades  and  compute  a  single  set  of 
correction  numbers  for  each  test. 

The  grade  medians  calculated  from  the  distributions  of  the  scores  yielded 
by  the  different  forms  furnished  additional  information  concerning  the  degree 
of  their  equivalence.  This  information  is  not  in  complete  agreement  with  that 
obtained  by  the  study  described.  Although  it  is  less  accurate  it  deserves  some 
consideration  in  the  formulation  of  a  set  of  rules  for  translating  the  scores 
obtained  from  one  form  to  the  basis  of  another  form.  In  Table  IX-A  grade 
medians  for  all  forms  are  given,  and  in  Table  IX-B  correction  numbers  which 
may  be  used  in  reducing  scores  from  Form  2  or  Form  3  to  Form  1.  The  cor- 
rection numbers  are  based  primarily  on  the  results  of  the  study  just  described 
but  some  weight  was  given  to  the  information  furnished  by  the  tabulations  of 


TABLE  IX-A.    MONROE 'S  STANDARDIZED  SILENT  READING  TESTS.    GRADE 
MEDIANS  FOR  JANUARY  AND  JUNE  TESTING,  BASED  UPON  130,000  SCORES 


GRADE 


III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

FORM  1 

Rate 

January 

52 

70 

87 

90 

100 

106 

83 

85 

90 

96 

June 

60 

79 

94 

96 

104 

108 

86 

87 

94 

100 

Comprehension 

January 

6.8 

12.7 

17.8 

18.5 

22.8 

26.0 

23.0 

25.4 

27.2 

30.0 

June 

9.3 

15.3 

20.8 

21.0 

24.5 

27.3 

24.0 

26.0 

28.6 

32.0 

FORM  2 

Rate 

January 

63 

77 

98 

116 

130 

133 

84 

90 

98 

104 

June 

70 

88 

106 

124 

132 

136 

86 

92 

101 

109 

Comprehension 

January 

8.3 

13.3 

17.2 

18.1 

26.0 

28.2 

25.4 

28.0 

31.0 

33.1 

June 

10.6 

15.6 

20.5 

20.8 

27.3 

29.4 

26.6 

29.4 

32.2 

34.5 

FORM  3 

Rate 

January 

78 

92 

97 

101 

109 

111 

June 

85 

95 

104 

106 

111 

114 

Comprehension 

January 

9.3 

14.8 

18.4 

22.2 

26.5 

29.8 

June 

11.9 

16.8 

21.5 

24.4 

28.2 

30.5 

22 

TABLE  IX-B.  APPROXIMATE  CORRECTIONS  BY  WHICH  TO  MULTIPLY  FORM  2 
AND  FORM  3  SCORES  TO  REDUCE  TO  THE  BASIS  OF  FORM  1  SCORES 


RATE 


COMPREHENSION 


Test  I 

Test  II 

Test  III 

Test  I 

Test  II 

Test  III 

Form  2            .  88 
Form  3            .  78 

.80 
.93 

.94 

.95 
.94 

.93 
.86 

.90 

the  scores  obtained  from  the  different  forms.     This  is  the  explanation  of  some 
apparent  inconsistencies  in  the  reductions  to  the  basis  of  Form  1. 

It  should  be  noted  that  the  scores  of  the  different  tests  in  this  series  are 
not  comparable.  This  is  to  be  expected  in  the  case  of  the  rate  scores  but  in 
the  case  of  the  comprehension  scores  an  effort  was  made  to  have  the  different 
tests  yield  comparable  scores.  This  attempt  was  not  successful. 

The  grade  distributions  which  are  not  published  here,  show  that  the  tests 
are  too  short  for  the  time  allowed.  In  order  to  secure  accurate  measures  of 
the  abilities  of  the  best  readers  it  will  be  necessary  either  to  lengthen  the  test 
or  to  shorten  the  time  allowed.  The  wide  spread  use  of  these  tests  has  revealed 
other  defects.  Instead  of  attempting  to  remedy  these  defects  in  the  present 
series  it  was  decided  to  derive  an  entirely  new  series.  These  have  been  issued 
under  the  title  of  "Monroe's  Standardized  Silent  Reading  Tests,  Revised." 
Three  forms  of  Tests  I  and  II  are  now  available.  They  were  originally  pub- 
lished as  a  part  of  the  Illinois  Examination  but  are  now  printed  separately. 

In  Tables  X-A  and  X-B  we  have  assembled  a  miscellaneous  collection 
of  grade  medians.  These  are  published  because  a  number  of  requests  have 
been  received  for  just  this  type  of  information. 

REFERENCES 

Monroe,  W.  S.,  "Monroe's  Standardized  Silent  Reading  Tests,"     Journal  of  Edu- 
cational Psychology,  IX,  (June,  1918),  303-312. 

The  deriviation  of  the  tests  more  or  less  based  upon  the  Kansas  Silent  Reading  Test  plan, 
is  briefly  sketched.  The  investigation  of  weighting  and  timing  is  outlined,  a  sample  of  the 
tests  is  given  and  some  few  data  concerning  results  from  pupils. 

Barnes,  Harold,     "Reorganization  of  Classes  Based  on  the  Monroe  Silent  Reading 
Tests,"     University  of  Pennsylvania  Bulletin,  vol.  XX,  No.  1,  119-123. 

This  article  recounts  the  use  made  of  these  tests  in  the  elementary  grades  of  Girard  College. 
Not  only  are  the  scores  presented,  but  also  the  resulting  organization  upon  the  basis  of  ability 
as  shown  on  the  tests  is  described. 

Kelly,  F.  J.,     "Kansas  Silent  Reading  Tests,"    Journal  of  Educational  Psychology > 
VII,  (February,  1916),  63-80. 

The  author  of  these  tests,  which  were  the  forerunners  of  Monroe's  Standardized  Silent  Reading 
Tests,  gives  a  brief  statement  of  the  construction,  administration,  and  use  of  the  tests,  follow- 
ing it  with  a  more  detailed  statement  of  results  secured  in  nineteen  Kansas  cities. 

Lloyd,  S.  M.  and  Gray,  C.  T.,     "Reading  in  a  Texas  City,  Diagnosis  and  Remedy,"" 
University  of  Texas  Bulletin,  No.  1853. 


23 

This  bulletin  gives  an  account  of  a  study  of  the  reading  situation  in  Austin.  The  Monroe 
tests  were  given  in  grades  3-7.  Results  obtained  are  analyzed  at  considerable  length, 
measures  to  improve  the  situation  are  discussed,  and  improvement  after  a  period  of  special 
emphasis  on  reading  is  shown. 

Pressey,  S.  L.  and  L.  W.,  "The  Relative  Value  of  Rate  and  Comprehension  Scores 
in  Monroe's  Silent  Reading  Test,  as  Measures  of  Reading  Ability,"  School  and  Society. 
(June  19,  1920),  747-49. 

In  a  brief  discussion  of  the  above  subject,  the  writers  present  results  of  correlating  teachers' 
estimates  of  reading  ability  with  rate  and  comprehension  scores,  also  the  latter  with  each 
other.  They  conclude  that  comprehension  scores  may  tell  us  all  the  tests  can  about  children's 
ability  in  reading. 


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25 


E.     CHARTERS  DIAGNOSTIC  LANGUAGE  TESTS,  AND  DIAGNOSTIC 
LANGUAGE  AND  GRAMMAR  TESTS. 

There  are  two  groups  of  these  tests:  (1)  The  Diagnostic  Language 
Tests,  designed  for  Grades  III  to  VIII  inclusive,  which  include,  Pronouns, 
Verbs,  (formerly  Verbs  A),  Miscellaneous  A  (formerly  Miscellaneous),  Mis- 
cellaneous B  (formerly  Verbs  B);  (2)  The  Language  and  Grammar  Tests, 
designed  for  Grades  VII  and  VIII,  which  include  Pronouns,  Verbs  (formerly 
Verbs  A)  and  Miscellaneous  A  (formerly  Miscellaneous).  The  Language 
Tests  consist  of  a  number  of  sentences  most  of  which  are  grammatically  in- 
correct. If  a  sentence  is  correct  the  pupil  makes  a  cross  on  the  dotted  line 
below  the  sentence.  If  the  sentence  is  not  right  the  pupil  is  required  to  put 
the  correct  words  on  the  dotted  line  below  it.  In  the  Language  and  Grammar 
Tests  the  pupil  is  required  in  addition  to  write  the  rule  on  which  the  correction 
is  based.  The  pupil 's  score  is  the  number  of  exercises  which  he  does  correctly. 
Since  the  sentences  which  make  up  the  tests  were  selected  as  representative 
of  the  errors  which  pupils  make,  a  pupil 's  performance  on  the  tests  gives  a 
diagnosis  of  his  abilities  in  the  field  of  these  tests. 

There  are  two  forms  of  these  tests.  The  second  form,  however,  was  not 
published  until  September,  1920.  Consequently,  the  scores  reported  in  this 
bulletin  are  based  on  Form  1.  Although  the  two  forms  were  constructed  so  that 
Form  2  might  be  expected  to  be  equivalent  to  Form  1,  there  is  available  at 
this  time  no  information  concerning  the  degree  of  their  equivalence. 

TABLE  XI   A.    GRADE  NORMS  FOR  CHARTERS'   DIAGNOSTIC  LANGUAGE 
TESTS.    MARCH  TESTING 


GRADES 

III 

IV 

V 

VI 

VII 

VIII 

*MlSCELLANEOUS  A 

Number  of  Pupils 

386 

669 

668 

845 

758 

494 

25-percentile 

4.0 

5.8 

8.1 

11.8 

14.0 

16.6 

Median 

6.7 

9.3 

11.6 

16.5 

18.9 

22.3 

75-percentile 

13.3 

13.6 

16.0 

21.7 

24.4 

27.1 

fMlSCELLANEOUS  B 

Number  of  Pupils 

230 

430 

307 

475 

412 

294 

25-percentile 

3.0 

10.6 

15.7 

19.8 

23.5 

28.7 

Median 

7.9 

17.8 

22.0 

27.3 

29.4 

32.0 

75-percentile 

14.8 

24.5 

27.6 

32.4 

33.7 

36.8 

**VERBS 

Number  of  pupils 

365 

403 

373 

478 

539 

638 

25-percentile 

7.3 

12.9 

17.2 

19.0 

22.7 

28.6 

Median 

12.6 

17.7 

22.6 

24.3 

27.7 

32.8 

75-percentile 

18.8 

22.7 

28.4 

29.3 

31.9 

36.1 

PRONOUNS 

Number  of  pupils 

787 

864 

895 

1344 

1566 

1253 

25-percentile 

8.9 

11.1 

14.2 

17.0 

19.6 

23.1 

Median 

13.6 

15.1 

18.5 

21.4 

24.5 

29.0 

75-percentile 

19.8 

20.3 

22.6 

25.7 

29.5 

34.0 

*  Formerly  Miscellaneous 
t  Formerly  Verbs  B 
**  Formerly  Verbs  A 


26 


TABLE  XI-B.    GRADE  NORMS  FOR 

CHARTERS'  DIAGNOSTIC  LANG- 

GUAGE  AND  GRAMMAR  TESTS 

MARCH  TESTING 


GRADES 

VII 

VIII 

MISCELLANEOUS 

Number  of  pupils 

332 

362 

25-percentile 

2.9 

6.1 

Median 

6.3 

11.9 

75-percentile 

11.7 

18.7 

VERBS 

Number  of  pupils 

434 

497 

25-percentile 

2.8 

6.9 

Median 

7.8 

14.0 

75-percentile 

22.9 

24.1 

PRONOUNS 

Number  of  pupils 

332 

362 

25-percentile 

4.4 

8.5 

Median 

8.0 

17.1 

75-percentile 

16.7 

26.0 

REFERENCES 

Charters,  W.  W.,     "Minimum  Essentials  in  Elementary  Language  and  Grammar," 
Sixteenth  Yearbook  of  the  National  Society  for  the  Study  of  Education.     Part  I,  85-110. 
This  article  gives  a  brief  account  of  a  number  of  studies  of  language  and  grammar  errors  made 
by  school  children,  with  tables  of  results.     These  studies  were  the  basis  of  the  content  of 
Charters'  tests. 

Sixth  Conference  on  Educational  Measurements.     Bulletin  of  the  Extension  Division, 
Indiana  University,  Vol.  V,  No.  I,  pp.  6-12  and  13-24. 

These  two  discussions  by  Charters  give  a  rather  general  discussion  leading  up  to  a  brief 
account  of  the  development  and  form  of  the  tests,  followed  by  some  suggestions  as  to  their  use. 

Charters,   W.   W.,     "Constructing   a   Language   and   Grammar   Scale,"     Journal  of 
Educational  Research,  I  (April,  1920),  249-257. 

The  tests  herein  considered  are  a  revision  of  those  referred  to  above.  The  writer  gives  a 
short  description  of  their  derivation,  use,  scoring,  etc.  The  question  of  weighting  is  discussed 
and  the  reason  for  its  elimination  given. 


F.     WILLING  's  SCALE  FOR  MEASURING  WRITTEN  COMPOSITION 

The  Willing  Scale  for  Measuring  Written  Composition  differs  from  other 
composition  scales  in  that  an  attempt  is  made  to  secure  separate  measures  of 
"form  value "  and  "story  value. "  The  "  form  value "  of  a  pupil 's  composition 
is  based  upon  his  errors  in  grammar,  punctuation,  capitalization,  and  spelling. 
In  order  to  make  the  scores  in  form  value  comparable,  the  number  of  errors 
which  the  pupil  makes  is  multiplied  by  100  and  divided  by  the  number  of  words 
in  his  composition.  The  quotient  is  the  number  of  errors  per  hundred  words. 
The  "story  value"  of  a  pupil 's  composition  is  its  value  when  errors  of  grammar 
punctuation,  capitalization,  and  spelling  are  neglected.  This  value  is  measured 
by  means  of  the  scale. 


27 

TABLE  XII.    GRADE  NORMS   FOR  WILLING 'S  SCALE  FOR   MEASURING 
WRITTEN    COMPOSITION,    MARCH    TESTING 


GRADE 

III 

IV 

V 

VI 

VII 

VIII 

APPROX.  No.  OF  PUPILS 

325 

580 

705 

695 

570 

130 

STORY  VALUE 

25-percentile 

30.5 

43.4 

55.7 

60.9 

65.9 

65.3 

Median 

41.5 

58.7 

68.1 

74.0 

76.6 

79.0 

75-percentile 

54.8 

74.5 

78.8 

85.2 

86.6 

86.2 

FORM  VALUE  (Errors  per  100  Words) 

25-percentile 

11.7 

6.2 

3.6 

3.2 

2.6 

2.3 

Median 

18.5 

10.7 

6.8 

5.8 

4.4 

4.4 

75-percentile 

26.0 

17.3 

10.9 

9.8 

6.4 

7.0 

The  grade  distributions  given  in  Tables  XIII  and  XIV  indicate  that 
the  scale  needs  to  be  extended  at  both  ends.  It  does  not  contain  steps  low 
enough  in  story  value  to  provide  adequate  measures  for  many  compositions 
contributed  by  pupils  in  the  third  and  fourth  grades.  Neither  does  it  provide 
adequate  measures  for  the  best  compositions  in  grades  beyond  the  fourth. 
For  practical  purposes  these  limitations  are  not  serious  because  when  a  pupil's 
composition  is  as  poor  as  20  on  this  scale  the  pupil  needs  special  attention. 
When  a  pupil  writes  a  composition  as  good  as  90  on  this  scale  it  is  likely  that 
special  instruction  is  superfluous.  In  addition  it  may  be  pointed  out  that  the 
median  score  of  a  class  is  probably  not  affected  by  these  limitations  of  the  scale. 


TABLE  XIII.  WILLING 'S  SCALE   FOR   MEASUR- 
ING WRITTEN  COMPOSITION.  GRADE  DISTRI- 
BUTIONS FOR  MARCH  TESTING 


GRADE 


Story  Value 

Score* 

IV 

V 

VI 

VII 

VIII 

IX 

90 

7 

28 

52 

81 

95 

14 

80 

6 

67 

105 

177 

141 

48 

70 

8 

91 

168 

147 

150 

25 

60 

28 

91 

146 

123 

107 

21 

50 

60 

98 

110 

75 

41 

12 

40 

60 

90 

77 

49 

31 

4 

30 

75 

66 

39 

32 

5 

4 

20 

76 

48 

8 

8 

o 
J, 

1 

Total 

320 

579 

705 

692 

572 

129 

Median 

41.5 

58.7 

68.1 

74.0 

76.6 

79.0 

These  intervals  are  expressed  in  terms  of  their  mid- 
points. 

REFERENCES 

Willing,  M.  H.,    "The  Measurement  of  Written  Composition  in  Grades  IV  to  VIII. 
English  Journal,  VII  (March,  1915),  193-202. 


28 

The  writer  explains  and  outlines  the  measurement  of  written  composition  especially  in  con- 
nection with  the  Denver  and  Grand  Rapids  surveys.  The  method  of  constructing  the  scale, 
its  use,  scoring,  results  obtained,  etc.  are  discussed,  and  the  scale  reproduced. 

The  Denver  Survey,  1916,  Part  II,  pp.  59-63,  and  the  Grand  Rapids  Survey,  1916,  pp. 
85-105,  give  accounts  of  the  use  of  this  scale.  The  latter  contains  rather  complete  tables  and 
graphs  of  pupil  achievement,  and  comparisons  of  results  with  those  obtained  in  Denver 


TABLE  XIV.  WILLING 'S  SCALE  FOR  MEASURING 
WRITTEN    COMPOSITION.  GRADE    DISTRI- 
BUTIONS FOR  MARCH  TESTING 


GRADE 

IV 

V 

VI 

VII 

VIII 

IX 

30 

50 

14 

3 

5 

2 

27 

24 

17 

1 

4 

3 

24 

22 

27 

8 

4 

2 

21 

32 

29 

9 

4 

1 

18 

43 

38 

19 

18 

4 

15 

29 

51 

45 

17 

15 

2 

12 

42 

56 

52 

48 

28 

4 

9 

34 

120 

105 

96 

49 

12 

6 

32 

79 

149 

140 

131 

21 

3 

14 

98 

170 

199 

200 

49 

0 

5 

41 

141 

158 

138 

41 

Total 

327 

570 

702 

693 

573 

129 

Median 

18.5 

10.7 

6.8 

5.8 

4.5 

4.4 

*  Errors  per  100  words. 

G.    HARLAN'S  TEST  FOR  INFORMATION  IN  AMERICAN  HISTORY 

This  test  consists  of  ten  exercises  in  the  field  of  American  History  and 
is  designed  for  use  in  the  seventh  and  eighth  grades.  Each  exercise  consists 
of  two  or  more  parts.  The  maximum  score  which  a  pupil  may  receive  is  100. 


TABLE    XV.    GRADE    NORMS    FOR 

HARLAN'S  TEST  OF  INFORMATION 

IN  AMERICAN  HISTORY.    MAY 

TESTING 


VII 

VIII 

Number  of  pupils 
25-percentjle 
Median 
75-percentile 

1109 
30.1 
43.9 

57.3 

1691 

45.7 
68.2 
83.3 

GRADE 


In  Table  XVI  the  distributions  of  scores  for  the  seventh  and  eighth 
grades  are  given.     These  distributions  are  of  interest  because  of  the  very  great 


29 

individual  differences  which  they  suggest.  It  is  possible  that  the  apparent 
differences  are  due  in  a  considerable  measure  to  the  errors  of  measurement. 
Since  there  is  only  one  form  of  the  test  no  measure  of  reliability  is  available. 


TABLE    XVI.    HARLAN'S    TEST    OF 
INFORMATION    IN    AMERICAN 
HISTORY.    GARDE    DISTRI- 
BUTIONS FOR  MAY 
TESTING 


GRADE 

SCORE 

VII 

VIII 

96 

6 

66 

91 

3 

118 

86 

13 

140 

81 

18 

187 

7£ 

35 

136 

71 

35 

136 

66  t 

54 

112 

61 

65 

92 

56 

65 

100 

51 

99 

95 

46 

113 

79 

41 

115 

98 

36 

100 

90 

31 

93 

79 

26 

94 

61 

21 

79 

42 

16 

63 

35 

11 

37 

13 

6 

19 

10 

0 

3 

2 

TOTAL 

1109 

1691 

MEDIAN 

43.9 

68.2 

REFERENCES 

Harlan,  Chas.  L.,     "Educational  Measurement  in  The  Field  of  History,"    Journal  oj 
Educational  Research,  II  (December,  1920),  849-853. 

The  writer  follows  a  short  discussion  of  tests  in  the  "content"  subjects  with  a  brief  description 
of  his  test  and  its  use  in  nine  cities.  The  requirements  he  deems  essential  to  a  good  test  are 
listed  as  a  basis  of  his  test. 

Griffith,  G.  L.,     "  Harlan 's  American  History  Tests  in  the  New  Trier  Township  Schools," 
School  Review  (November,  1920),  697-708. 

The  first  half  of  this  article  is  devoted  to  a  general  discussion  of  history  and  history  testing. 
This  is  followed  by  a  description  of  the  test  and  the  results  of  its  use  in  the  eighth  grade  of 
this  township.  Data  are  given  for  each  of  the  single  exercises  of  the  test. 


H.     SACKETT'S  SCALE  IN  UNITED  STATES  HISTORY 

This  scale,  arranged  by  L.  W.  Sackett,  was  originally  devised  by  Bell 
and  McCollum.     It  consists  of  seven  tests  which  appear  to  have  been  intended 


30 

for  use  in  secondary  schools  and  colleges.  The  medians  given  in  Table  XVII 
are  for  the  eighth  grade.  The  number  of  scores  is  such  that  it  is  doubtful  if 
the  median  scores  have  much  value  for  use  as  tentative  standards. 


TABLE  XVII.    GRADE  NORMS  FOR  SACKETT'S  SCALE  IN  UNITED  STATES 
HISTORY.    MAY   TESTING.    EIGHTH    GRADE 


TESTS 

1 

I 

II 

III 

IV 

V 

VI 

VII 

Number  of  pupils 
25-percentile 

111 
62.6 

101 
50.8 

107 
69.2 

92 
37.0 

93 

44.7 

78 

7.5 

85 
9.6 

Median 

118.7 

146.2 

115.0 

125.0 

86.5 

46.6 

96.5 

75-percentile 

192.5 

273.9 

183.1 

287.5 

193.7 

138.1 

195.5 

REFERENCES 

Bell,  J.  C.  and  McCollum,  D.  F.  "A  Study  of  the  Attainments  of  Pupils  in  United 
States  History,"  Journal  of  Educational  Psychology,  VIII  (May,  1917),  257-74. 
The  writers  follow  a  discussion  of  historical  ability  with  an  account  of  the  use  of  test  material 
in  various  schools  from  Grade  V  through  the  senior  year  of  the  University  of  Texas.  The 
results  secured  are  analyzed.  The  test  questions  used  were  in  general  similar  in  kind  to  those 
of  Sackett 's  Scale  in  Ancient  History,  although  based  upon  United  States  History. 

Sackett,  L.  W.     "A  Scale  in  Ancient  History."    Journal  of  Educational  Psychology* 
VIII  (May,  1917),  284-93. 

The  test  questions  are  given  with  a  brief  statement  of  their  source,  use,  and  scoring.  Results 
are  given  from  almost  1000  papers,  and  the  relative  difficulty  of  the  questions  computed. 

Sackett,  L.  W.     "A  Scale  in  United  States  History,"    Journal  of  Educational  Psy- 
chology, X  (September,  1919),  345-348. 

The  writer  tells  of  the  development  of  this  scale  out  of  the  data  furnished  by  Bell  and  McCol- 
lum's  work  referred  to  above.  The  determination  of  the  relative  difficulty  of  the  parts  is 
given  considerable  space. 

I.    HOTZ'S  FIRST  YEAR  ALGEBRA  SCALE 

This  scale  consists  of  five  separate  scales :  ( 1 )  Addition  and  subtraction ; 
(2)  Multiplication  and  division;  (3)  Equation  and  formulae;  (4)  Problems; 
(5)  Graphs.  Each  sub-scale  consists  of  exercises  arranged  in  order  of  increasing 
difficulty. 


REFERENCES 

Hotz,  H.  G.     First  Year  Algebra  Scales,  Teachers  College,  Columbia  University,  Contri- 
butions to  Education  No.  90. 

The  writer  gives  a  history  of  the  derivation  of  these  scales,  a  complete  reproduction  of  them, 
and  a  discussion  of  their  administration  and  use.  The  statistical  working  out  of  the  scales 
is  treated  fully  for  one  of  them,  the  procedure  for  all  being  the  same. 

Cawl,  F.  R.     "Practical  Uses  of  an  Algebra  Standard  Scale,"      School  and  Society 
(July,  1919),  89-91. 

The  results  of  testing  a  class  in  a  large  private  school  are  here  presented.  The  matter  of 
correlation  with  English,  French,  and  Latin  is  considered.  A  short  interpretation  of  results 
is  given,  with  suggestions  as  to  the  value  of  using  such  a  scale. 


31 


TABLE    XVIII.    GRADE    NORMS     FOR 

HOTZ'S  FIRST  YEAR  ALGEBRA 

SCALES.    MAY  TESTING 


GRADE 

IX 

X 

ADDITION  AND  SUBTRACTION 

Number  of  pupils 

561 

390 

25-percentile 

5.2 

5.8 

Median 

6.9 

7.3 

75-percentile 
MULTIPLICATION  AND  DIVISION 

9.1 

8.7 

Number  of  Pupils 

570 

388 

25-percentile 

5.7 

5.9 

Median 

7.2 

7.4 

75-percentile 

8.4 

8.7 

EQUATIONS  AND  FORMULAS 

Number  of  Pupils 

478 

385 

25-percentile 

6.2 

6.7 

Median 

7.7 

7.9 

75-percentile 

9.7 

9.1 

PROBLEMS 

Number  of  Pupils 

566 

394 

25-percentile 

4.5 

3.9 

Median 

6.4 

5.0 

75-percentile 

8.6 

6.3 

GRAPHS 

Number  of  Pupils 
25-percentile 

121 

5.2 

413 
4.1 

Median 

6.2 

5.0 

75-percentile 

7.0 

6.0 

J.     MINNICK'S  GEOMETRY  TESTS 

This  series  of  tests  is  based  on  the  assumption  that  the  demonstration 
of  a  geometrical  theorem  involves  the  following  abilities:  Test  A,  the  ability 
to  draw  the  figure.  Test  B,  the  ability  to  state  the  hypothesis  and  conclusion. 
Test  C,  the  ability  to  recall  the  facts  concerning  the  figure.  Test  D, 
the  ability  to  select  and  organize  facts  so  as  to  produce  the  proof. 
Test  E,  the  ability  to  draw  auxiliary  lines.  The  series  includes  one  test  for 
each  of  these  abilities.  No  report  is  made  for  Test  E.  These  tests  are  unique 
in  that  they  provide  for  both  positive  scores  and  negative  scores.  The  positive 
score  is  the  percent  of  the  necessary  elements  of  the  proof  given  correctly  by 
the  pupil.  The  negative  score  is  the  number  of  incorrect  and  unnecessary 
elements. 

REFERENCES 

Minnick,  J.  H.    An  Investigation  of  Certain  Abilities  Fundamental  to  the  Study  of  Geometry. 
University  of  Pennsylvania. 

This  monograph  gives  a  synopsis  of  methods  and  results  used  in  deriving  the  tests,  followed 
by  a  more  detailed  statement.  The  latter  includes  a  reproduction  of  the  tests,  tables  giving 
data  secured  from  testing,  statistical  methods  of  weighting  exericises,  suggestions  as  to  use,  etc. 


32 


TABLE  XIX.    GRADE  NORMS  FOR  MINNICK'S  GEOMETRY  TESTS 


Positive  Scores 
Grade 

Negative  Scores 
Grade 

X 

XI 

X 

XI 

TEST  A  (ability  to  draw  accurate  figures  for  theorems) 
Number  of  pupils                                                    « 
25-percentile 
Median 

126 
53.3 
63.0 

66 

43.8 
58.0 

126 
2.4 
4.1 

60 
1.1 
2.6 

75-percentile 

67.2 

69.2 

6.6 

5.4 

TEST  B  (Ability  to  state  hypothesis  and  conclusion  in 

terms  of  given  figure.) 
Number  of  Pupils 
25-percentile 
Median 

167 
55.2 
69.6 

66 
55.5 
67.1 

167 
1.1 

2.3 

66 
1.0 
2.0 

75-percentile 

81.3 

83.6 

3.9 

3.9 

TEST  C  (Ability  to  recall  known  facts  about  figures  when 

one  or  more  are  given). 

Number  of  Pupils 

154 

65 

154 

63 

25-percentile 
Median 

52.2 
64.1 

55.6 
64.7 

1.9 

3.8 

1.4 
3.9 

75-percentile 

77.2 

77.9 

7.1 

5.7 

TEST  D  (Ability  to  organize  and  select  facts  to  produce  a 

proof)  . 

Number  of  Pupils 
25-percentile 

155 
68.0 

68 
75.0 

155 
.8 

54 
.8 

Median 

85.5 

89.2 

1.6 

1.6 

75-percentile 

92.9 

98.3 

2.3 

3.2 

Minnick,  J.  H.     "A  Scale  for  Measuring  Pupil's  Ability  to  Demonstrate  Geometrical 
Theorems,"     School  Review,   (Feb.,    1919),   101-109. 

A  brief  account  of  the  construction  of  a  scale  to  measure  one  definite  geometric  ability  is  given. 
The  scores  made  upon  the  first  selection  of  exercises,  the  resultant  weighting  and  then  the 
selection  of  those  best  suited  to  make  up  a  scale  are  briefly  treated.  The  exercises  chosen  are 
reproduced. 

Minnick,  J.  H.     "Certain  Abilities  Fundamental  to  the  Study  of  Geometry,"     Journal 
of  Educational  Psychology,  (Feb.,  1918),  83-90. 

Four  abilities  requisite  to  formal  geometrical  demonstration  are  listed.  Their  relation  to 
teaching,  development  by  teaching,  and  diagnosis  by  tests  are  discussed.  The  tests  used 
were  those  of  the  author.  Correlations  with  teachers  marks  are  given. 

K.    HOLLEY'S  SENTENCE  VOCABULARY  SCALE 
This  scale  consists  of  a    number  of  exercises  of  the  following  type: 

1.  Impolite  people  are kindly brave young ill-bred. 

2.  A  man  is  afloat  in  a mine tower boat hospital. 

The  pupil  is  asked  to  underline  the  word  which  makes  the  truest  sentence. 
These  exercises  are  arranged  in  order  of  increasing  difficulty,  and  a  pupil's 
score  is  found  by  subtracting  one-third  of  the  number  of  errors  from  the  number 
correct.  An  abbreviated  form  of  this  scale  has  been  incorporated  in  the  Illinois 
General  Intelligence  Scale.  The  scale  was  constructed  to  provide  a  suitable 
means  of  ascertaining  the  general  intelligence  of  groups  of  children.  The 
measure  which  it  yields  is  not  sufficiently  accurate  to  be  used  as  an  index  of 
the  general  intelligence  of  individual  pupils.  The  scale  is  also  recommended  as 


33 

an  instrument  for  measuring  the  vocabulary  of  pupils.  The  total  distributions 
given  in  Table  XXI  indicate  that  this  scale  is  too  difficult  for  pupils  in  the 
third  and  fourth  grades. 

TABLE  XX.  GRADE  NORMS  FOR  HOLLEY'S  SENTENCE  VOCABULARY  SCALE 

APRIL  TESTING 


GRADE 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

Number  of  pupils 
25-percentile 
Median 
75-percentile 

406 
8.4 
16.6 

28.5 

520 
16.7 
25.1 
33.6 

465 
25.3 
33.0 
39.9 

450 
33.4 
42.8 
51.5 

1188 
32.3 
41.9 
49.7 

1047 
40.1 

47.7 
55.8 

253 
40.9 
49.0 
57.1 

223 
50.1 
56.0 
63.5 

155 

52.4 
59.9 
67.9 

108 

54.5 
62.7 
70.1 

REFERENCES 

Terman,  L.  M.  and  Childs,  H.  G.  "A  Tentative  Revision  and  Extension  of  the  Binet- 
Simon  Measuring  Scale  of  Intelligence,"  Journal  of  Educational  Psychology,  (April,  1912), 
205-208. 

The  basis  of  Holley's  Sentence  Vocabulary  Scales  is  the  Stanford  Revision,  100  word  Vocabu- 
lary Test,  the  construction  of  which  is  here  described.  Tentative  standards  of  achievement 
are  also  given. 

Holley,  C.  E.  Menial  Tests  for  School  Use.  Bureau  of  Educational  Research,  Uni- 
versity of  Illinois,  Bulletin  No.  4  pp.  86-91. 

This  bulletin  gives  an  account  of  a  comparative  study  of  six  group  intelligence  scales,  of  which 
the  above  was  one,  based  on  data  from  the  school  system  of  Champaign,  Illinois.  A  brief 
account  of  the  origin  of  the  Sentence  Vocabulary  Scales  is  included  (p.  30). 

Branson,  E.  P.  "An  Experiment  in  Arranging  High-School  Sections  on  the  Basis 
of  General  Ability,"  Journal  of  Educational  Research,  (Jan.,  1921),  53-56. 
At'Long  Beach,  California,  this  scale  was  given  to  two  groups  of  high-school  entrants  who  had 
recently  taken,  and  been  grouped  by  the  Otis  Group  Intelligence  Scale.  At  the  end  of  the 
term  the  test  was  repeated.  A  comparison  by  groups  of  the  scores  at  the  two  periods,  and 
correlations  with  the  Otis  Scale,  are  given. 


TABLE  XXI.    HOLLEY'S  SENTENCE  VOCABULARY  SCALE.    GRADE  DISTRI- 
BUTIONS    FOR     APRIL     TESTING 


GRADE 


III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

90 

6 

80 

5 

1 

2 

7 

70 

3 

1 

8 

21 

27 

21 

60 

1 

5 

50 

75 

126 

32 

56 

48 

36 

50 

31 

4 

20 

74 

199 

321 

79 

85 

52 

31 

40 

18 

44 

89 

141 

379 

341 

78 

45 

23 

13 

30 

42 

128 

170 

110 

290 

153 

50 

15 

3 

20 

71 

170 

137 

59 

123 

73 

5 

10 

124 

130 

30 

13 

74 

29 

1 

0 

120 

43 

14 

3 

34 

3 

TOTAL 

406 

520 

465 

450 

1188 

1047 

253 

223 

155 

108 

MEDIAN 

16.7 

25.1 

33.0 

42.8 

41.9 

47.8 

49.0 

56.0 

59.9 

62.7 

34 

L.     HOLLEY'S  PICTURE  COMPLETION  TEST  FOR  PRIMARY  GRADES 

This  test,  as  it  name  suggests,  consists  of  a  number  of  pictures  which  are 
incomplete.  The  pupil  is  expected  to  add  the  part  which  is  missing.  It  was 
designed  as  an  instrument  for  measuring  the  general  intelligence  of  young 
children.  The  total  distributions  as  given  in  Table  XXIII  indicate  that  it  is 
not  a  good  instrument  for  this  purpose.  The  distributions  exhibit  unusually 

TABLE  XXII.    GRADE  NORMS  FOR  HOLLEY'S  PICTURE  COMPLETION  TEST 
FOR  PRIMARY  GRADES.    JANUARY  TESTING 


GRADE 

Kinder- 
garten 

I 

II 

III 

327 
9.9 
13.5 
16.5 

IV 

167 
8.8 
12.3 
15.0 

Number  of  pupils 
25-percentile 
Median 
75-percentile 

75 
1.8 
5.3 
7.8 

1438 
4.4 
7.8 
12.2 

1233 
7.9 
11.5 
15.1 

TABLE  XXIII.    HOLLEY'S  PICTURE 
COMPLETION  TEST  FOR  PRIMARY 
GRADES.    GRADE  DISTRIBU- 
TIONS FOR  JANUARY 
TESTING 


GRADE 

SCORE 

I 

II 

III 

IV 

20 

34 

31 

9 

4 

19 

23 

43 

13 

4 

18 

33 

46  * 

25 

9 

17 

36 

59 

20 

12 

16 

42 

64 

27 

3 

15 

52 

72 

34 

10 

14 

47 

76 

22 

15 

13 

54 

88 

26 

14 

12 

48 

98 

24 

17 

11 

82 

77 

19 

14 

10 

72 

92 

24 

9 

9 

81 

84 

24 

12 

8 

91 

89 

26 

9 

7 

103 

75 

11 

11 

6 

122 

59 

9 

13 

5 

94 

50 

8 

8 

4 

112 

50 

4 

2 

3 

108 

29 

1 

1 

2 

86 

21 

1 

1 

77 

28 

0 

41 

2 

TOTAL 

1438 

1233 

327 

167 

MEDIAN 

7.8 

11.5 

13.5 

12.3 

35 


high  variability.  This  is  much  greater  than  is  exhibited  by  other  tests  when 
applied  to  children  in  these  grades.  The  median  scores  given  in  Table  XXII 
give  further  indications  of  the  inadequacy  of  this  test,  particularly  in  the  grades 
above  the  first. 

REFERENCES 

Holley,  C.  E.     Mental  Tests  for  School  Use.     Bureau  of  Educational  Research,  University 
of  Illinois,  Bulletin  No.  4,  pp.  86-91. 

A  general  discussion  of  tests  of  this  type  is  followed  by  an  account  of  the  testing  from  which 
this  test  came.  This  was  done  in  Champaign,  Illinois.  Results  are  merely  outlined. 


CHAPTER  III 

THE  DERIVATION  OF  MONROE*S  STANDARDIZED  REASONING 
TESTS  IN  ARITHMATIC4 

The  process  of  problem  solving."  Reasoning  "as it  occurs  in  the  solving 
of  an  arithmetical  problem  involves  these  steps:  (1)  A  careful  reading  of  the 
problem  including  the  association  of  correct  arithmetical  meanings  with  the 
"technical"  terms  used  in  stating  the  problem.  (2)  Recall  of  facts  and  prin- 
ciples suggested  by  the  problem  and  required  for  its  solution.  (3)  Formulation 
of  a  hypothesis  or  plan  of  solution  using  as  data  the  results  of  the  first  two  steps. 
(4)  Verification  of  this  plan  of  solution.  This  process  of  reasoning  is  usually 
followed  by  the  calculations  outlined  in  the  plan  of  solution.  This  additional 
step,  however,  is  not  a  part  of  the  reasoning  process. 

Two  kinds  of  words  are  used  in  stating  arithmetical  problems:  (1) 
The  descriptive  words  give  the  setting  of  the  problem.  Only  in  an  indirect 
way  do  these  affect  the  solution.  (2)  The  "technical  terms"  of  an  arithmetical 
problem  consist  of  those  words  and  phrases  which  define  quantities  and  quan- 
titative relationships.  Every  problem  involves  at  least  three  quantities, 
two  given  and  the  third  to  be  found.  These  quantities  are  related  in  a  definite 
way.  For  example,  the  sum  of  the  two  quantities  given  equals  the  third,  or 
the  third  is  the  quotient  of  one  divided  by  the  other.  In  problems  involving 
two  or  more  steps  there  are  more  than  three  quantities  and  the  relationships 
are  more  complex.  However,  in  every  case  there  are  words  or  phrases  which 
either  directly  or  indirectly  tell  what  these  relationships  are,  and,  consequently, 
what  operations  must  be  performed  to  obtain  the  desired  answer. 

This  principle  may  be  illustrated  by  the  following  problems:  "What 
are  the  average  daily  earnings  of  a  boy  who  receives  $0.88,  $0.25,  $1.15,  $0.75, 
$0.50,  and  $0.60  in  one  week?" 

The  phrase  "average  daily  earnings"  names  the  quantity  to  be  found 
and  also  specifies  its  relationship  with  the  given  quantities.  The  "average"  is 
the  quotient  of  the  sum  of  the  several  amounts  divided  by  the  number  of  items. 
A  knowledge  of  this  definite  meaning  of  "average"  is  necessary  if  one  is  form- 
ulating a  rational  plan  of  solving  the  problem.  If  the  phrase  "average  daily" 
was  omitted  we  would  have  an  entirely  different  problem. 

"How  many  square  yards  of  linoleum  will  be  required  to  cover  a  floor 
16  feet  by  12  feet?" 

"How  many  square  yards"  names  the  third  quantity  in  this  problem 
and  in  connection  with  "  15  feet  by  12  feet"  specifies  the  relations  which  exist 


4A  number  of  considerations  on  which  the  derivation  of  these  tests  is  based  are  con- 
tained in  an  article  by  the  writer  in  School  and  Society,  Volume  VIII,  pages  295  and  424. 
Sample  copies  of  these  tests  may  be  obtained  from  the  Public  School  Publishing  Company, 
Bloomington,  Illinois. 


37 

between  the  quantities.  This  third  quantity  is  the  product  of  the  dimensions 
divided  by  nine.5  In  this  case  the  number  of  square  feet  in  a  square  yard  must 
be  remembered  and  also  the  principle  that  the  area  of  a  rectangle  (i.e.,  a  figure 
whose  dimensions  are  given  as  in  the  problem)  is  the  product  of  the  length  by 
the  width. 

In  many  cases  when  the  first  two  steps  of  the  reasoning  process  have 
been  completed  satisfactorily,  the  formulation  of  the  plan  of  solution  (the  next 
step  in  the  reasoning  process)  involves  little  uncertainty.  In  fact  it  is  essentially 
mechanical.  This  is  the  case  in  these  illustrations.  In  the  case  of  very  simple 
problems,  or  very  familiar  problems,  the  reasoning  process  is  usually  short- 
circuited  so  that  there  is  no  explicit  association  of  meaning  with  the  technical 
terms  nor  recall  of  principles.  The  problem  as  a  whole  or  some  feature  of  it 
serves  as  a  cue  for  the  direct  association  of  the  plan  of  solution.  In  such  cases 
there  is  strictly  speaking,  no  reflective  thinking  or  reasoning,  and  the  mental 
process  involved  is  much  the  same  as  that  which  occurs  in  the  operations  of 
arithmetic.  The  solution  of  the  problem  has  become  automatic. 

The  nature  of  a  reasoning  test  in  arithmetic.  A  reasoning  test  in 
arithmetic  is  essentially  a  test  of  careful  reading  in  a  limited  field  to  answer 
specific  questions.  In  this  reading,  technical  vocabulary  is  fundamental. 
The  pupil  gives  evidence  of  his  degree  of  comprehension  by  his  plan  of  solution. 
The  correctness  of  the  numerical  answer  to  the  problem  depends  upon  the  ac- 
curacy of  the  pupil 's  calculations  and  the  recall  of  denominate  number  facts 
as  well  as  upon  the  plan  of  solution.  The  plan>  or  principle,  of  the  solution 
and  not  the  accuracy  of  the  numerical  answer  is,  therefore,  the  measure'  of  the 
pupil 's  ability  to  reason  in  arithmetic.  Thus  in  describing  a  pupil 's  perform- 
ance on  a  reasoning  test,  errors  in  the  recall  of  facts  and  in  calculation  should 
be  disregarded.  For  the  problems  which  are  solved  correctly  in  principle  a 
score  based  on  correct  answers  may  be  used  as  a  crude  measure  of  the  pupil 's 
ability  to  perform  the  operations  of  arithmetic. 

In  order  that  a  pupil's  score  on  a  reasoning  test  may  be  indicative  of 
his  ability  to  solve  arithmetical  problems  in  general,  the  problems  must  be 
carefully  selected  with  reference  to  content  (vocabulary).  The  ideal  reasoning 
test  would  be  one  that  included  all  of  the  technical  terms  but  this  is  not  possible 
because  the  vocabulary  of  arithmetical  problems  is  extremely  varied  and  volum- 
inous. In  another6  place  the  writer  has  reproduced  28  different  forms  of  state- 
ment which  were  found  in  the  examination  of  eight  text-books  for  the  problem, 
"Given,  $7.50,  paid  for  silk,  and  price  per  yard  $1.50,  to  find  the  number  of 
yards  purchased. "  This  condition  makes  it  necessary  to  select  a  few  problems 
which  will  be  representative  in  respect  to  content,  in  order  to  have  a  test  of 
usable  length. 

6An  alternative  solution  is  to  reduce  each  dimension  to  yards  before  finding  the  area. 
6Monroe,  Walter  S.     Measuring  the  Results  of  Teaching,  Houghton  Mifflin    Company 


38 

Method  of  selecting  problems  on  basis  of  content.  In  the  case  of  the 
series  of  tests  described  in  this  report  the  representative  problems  were  selected 
by  the  following  method.  The  one-  and  two-step  problems  appearing  in  eight 
widely  used  texts  were  classified  according  to  the  operation  or  operations  they 
called  for.  This  gave  in  one  group  all  the  problems  requiring  only  addition, 
in  another  those  requiring  only  subtraction  and  so  on.  The  problems  in  each 
of  these  groups  were  further  classified  by  the  writer  on  the  basis  of  the  technical 
terms  used.  This  was  found  to  be  difficult  because  of  the  great  variety  of 
these  terms.  Since  the  classification  represents  the  judgment  of  only  one  person, 
it  cannot  be  considered  final  in  any  sense. 

The  general  plan  of  classification  may  be  illustrated  by  the  types  of 
division  problems.  In  the  list  on  the  following  pages  only  those  types  are  given 
which  included  problems  found  in  five  or  more  of  the  eight  texts  examined. 
A  large  number  of  additional  types  included  problems  from  less  than  a  majority 
of  the  texts.  A  descriptive  statement  of  the  type  is  followed  by  a  limited 
number  of  illustrative  problems.  It  will  be  noted  that  for  a  single  type  these 
problems  are  not  identical  in  vocabulary  but  it  was  the  judgment  of  the 
writer  that  they  were  sufficiently  similar  to  justify  grouping  them  together. 
It  has  been  assumed  that  the  terms  used  are  essentially  synonymous.  This 
hypothesis  is,  of  course,  subject  to  experimental  verification.  Unfortunate- 
ly, this  is  lacking  at  this  time.  However,  the  resulting  list  of  type  prob- 
lems is  more  representative  of  the  vocabulary  of  arithmetical  problems  as  they 
occur  in  our  texts  than  any  other  available  list. 

DESCRIPTION  OF  TYPES  AND  ILLUSTRATIVE  PROBLEMS: 

1.  Given  a  whole  to  find  number  of  parts  of  a  given  size,  including 
to  find  the  number  of  acres  to  produce  a  given  yield. 

A  baker  used  three-fifths  Ibs.  of  flour  to  a  loaf  of  bread.     How  many  loaves 
could  he  make  from  a  barrel? 

When  the  average  yield  per  acre  is  25  bushels  how  many  acres  will  yield  925 
bushels. 

How  many  lengths  three-fourths  yds.  long  can  be  cut  from  15  yds.  of  goods? 

How  many  hens  can  be  properly  accommodated  in  a  pen  containing  51  square 
feet,  if  each  hen  requires  6  square  feet? 

964  marbles  are  distributed  equally  among  a  certain  number  of  boys.     Each 
boy  has  82  marbles.     How  many  boys  are  there? 

At  7>£  gallons  to  the  cubic  foot,  how  many  cubic  feet  will  3000  gallons  of 
oil  occupy? 

Oats  weigh  32  Ibs.  to  a  bushel.     How  many  bushels  are  there  in  a  load  weigh- 
ing 1344  Ibs? 

2.  Given  cost  and  price  to  find  the  number  of  articles  purchased.     This 
includes  wages  when  question  is  how  many  days,  weeks,  etc.  to  earn 
a  given  amount. 

At  16  cents  per  pound,  how  many  pounds  of  steak  does  a  woman  get  if  the 
amount  of  the  purchase  is  80  cents. 


3.  The  reverse  of  No.  1.     Given  whole  and  number  of  parts  to  find 
size  of  each  part. 

Three  boys  buy  a  rpwboat  for  twelve  dollars  and  seventy-five  cents,  sharing 
the  expense  equally.  Find  how  much  each  boy  has  to  pay. 

If  54  marbles  are  divided  equally  among  6  boys,  how  many  marbles  will  each 
receive? 

In  28  days  a  hotel  used  361  Ibs.  of  butter.     How  many  pounds  did  it  use  a  day? 

4.  The  reverse  of  No.  2. 

A  farmer  paid  thirty-three  dollars  and  a  half  for  4  bushels  of  seed  wheat.  How 
much  did  he  pay  for  a  bushel? 

The  bill  for  58  tons  of  copper  amounted  to  612  dollars.  What  was  the  price 
per  ton? 

A  fowl  weighing  4  and  one  half  Ibs.  sells  for  $1.00.     What  is  the  price  per  pound? 

A  man's  wages  amounted  to  46  dollars  for  9  and  one-fifth  day's  work.  How 
much  did  he  receive  per  day? 

A  man  works  8  hours  a  day  for  4  dollars  and  80  cents.  How  much  does  he 
receive  for  each  hour's  work? 

5.  Given  the  price  for  a  given  denomination  to  find  the  price  at  a  lower 
denomination. 

A  boy  bought  a  dozen  oranges  at  the  rate  of  15  cents  a  dozen.  What  did  they 
cost  him  apiece? 

When  milk  is  10  cents  a  quart,  how  much  is  a  pint  worth? 

6.  Given  the  whole  and  the  number  of  parts  to  find  the  average  (rate, 
price,  yield,  etc.) 

A  farmer  raised  500  bushels  of  wheat  on  a  field  of  40  acres.  What  was  the 
average  yield  per  acre? 

A  fast  train  runs  from  Chicago  to  a  station  356.4  mi.  distant  in  exactly  9  hours. 
What  is  the  average  rate  of  the  train? 

A  drover  paid  $1125  for  cows,  what  was  the  average  price  if  he  bought  25? 

A  mill  employs  600  hands  and  has  a  weekly  pay  roll  of  $2,000.  What  is  the 
average  weekly  wage  for  each  employee? 

7.  The  whole  and  the  rate  are  given.     The  question  is  asked  by,  "How 
long?" 

If  a  horse  eats  three-eights  bu.  of  oats  a  day,  how  long  will  6  bus.  last? 
How  long  will  it  take  to  earn  28  dollars  at  $1.75  a  day? 

8.  Given  distance  and  rate  to  find  how  long. 

At  25  miles  an  hour,  how  long  will  it  take  an  automobile  to  go  160  miles? 

9.  Given  distance  and  number  of  units  of  time  to  find  rate. 

In  3.2  hours  a  man  walks  12.32  mi.     How  far  does  he  walk  in  one  hour? 

Find  the  rate  of  speed  per  hour  made  by  an  airship  traveling  218.05  miles  in 
3.5  hour. 

10.     A  fractional  part  of  a  whole  is  given  to  find  the  whole. 

If,  when  18  and  three  eighths  mi.  of  track  are  laid,  one  third  of  the  road  is 
completed,  how  long  is  the  road? 

I  sold  a  bicycle  for  18  dollars.  This  was  three  sevenths  of  what  I  paid  for  it. 
How  much  did  I  pay  for  it  ? 


11.  A  percent  of  the  whole  is  given  to  find  the  whole. 

If  33  and  one  third  percent  of  a  man's  loss  is  300  dollars,  how  much  does  he 
lose? 

A  girl  spent  25  cents  which  was  12^  percent  of  her  monthly  allowance,  how 
much   was   her   allowance? 

A  clerk  had  his  weekly  wages  increased  3  dollars,  or  16  and  two  thirds  percent. 
What  were  his  wages  before  this  increase? 

12.  Given  the  amount  of  gain  or  profit  and  percent  of  gain  or  profit  to 
find  the  cost  or  selling  price. 

A  hardware  merchant  makes  a  profit  of  25  percent  or  32  cents  on  saws.     Find 
the  cost. 

A  farmer  sold  his  horse  at  a  gain  of  30  dollars,  or  25  percent.     Find  the  cost. 

13.  Given  the  commission  and  percent  of  commission  to  find  amount 
sold. 

Five  percent  commission  on  a  certain    amount  of  money  was  684.20  dollars. 
What  was  the  amount? 

14.  Given  two  numbers  to  find  what  percent  one  is  of  the  other. 

If  1000  Ibs.  of  potatoes  contain  180  Ibs.  of  starch,  what  percent  of  potatoes  is 
starch  ? 

If  a  man  saves  187.50  dollars  out  of  his  salary  of  1250  dollars,  what  percent 
does  he  save? 

The  boys  in  the  Marshall  school  won  5  of  the  8  games  of  hockey.    What  percent  ? 

In  his  examination  in  arithmetic  a  boy  had  10  problems  out  of  twelve  right. 
His  grade  was  what  percent? 

15.  Given  two  numbers  to  find  what  part  one  is  to  the  other. 

The  Jackson  basket-ball  team  won  35  out  of  56  games.     What  part  did  it  win? 

A  man  spends  for  rent  360  dollars  out  of  an  income  of  1 500  dollars.     What  part 
of  his  income  is  spent  this  way? 

16.  Given  the  amount  of  investment,  or  principle,  and  the  income  or 
interest  to  find  rate. 

Mrs.  Lynch  received  24  dollars  a  year  interest  on  400  dollars  loaned  Mrs~ 
Burnet.     What  is  the  rate? 

17.  Given  an  amount  in  one  denomination  to  reduce  to  a  higher. 

An  aviator  reaches  a  height  of  11,474  feet.     Express  this  height  in  miles. 
A  milk  dealer  sells  302  qts.  of  cream.     Express  this  as  gallons  and  quarts- 

In  digging  out  a  cellar  8260  cubic  feet  of  earth  were  removed.     At  27  cubic 
feet  to  the  cubic  yard,  how  many  cubic  yds.  were  removed? 

18.  Given  the  value  or  face  of  a  policy  and  premium  to  find  the  rate. 

Find  the  rate,  given  the  face  of  the  policy  as  1500  dollars  and  premium  1£ 
dollars. 

A  fire  insurance  company  charged  20  dollars  for  insuring  an  automobile  fas 
1000  dollars.     What  was  the  rate  of  insurance. 


41 


19.     Given  the  premium  and  rate  of  insurance  to  find  face  of  policy. 

A  man  paid  50  dollars  for  insuring  a  house,  the  rate  being  2  and  }A  percent. 
What  was  the  face  of  the  policy? 

Table  XXIV  gives  the  frequency  of  occurrence  of  each  type  in  each  of 
the  eight  texts  examined.  This  table  is  to  be  read  as  follows:  10  problems 
classified  as  belonging  to  Type  1  which  were  found  in  Text  1 ;  30  such  prob- 
lems were  found  in  Text  2;  20  in  Text  3;  34  in  Text  4,  etc.  The  total  number 
of  problems  classified  under  Type  1  is  147. 

The  variations  in  the  frequency  of  the  occurrence  of  problems  belonging 
to  a  single  type  are  worthy  of  notice.  Some  types  have  a  high  frequency  in 
certain  texts  while  in  other  texts  their  frequency  is  low  and  in  many  cases 
they  do  not  occur  at  all.  This  means  that  different  authors  have  tended  to 
use  different  vocabularies. 

TABLE   XXIV.    FREQUENCY  OF  OCCURRENCE  OF  TYPES  OF   PROBLEMS 
IN  DIVISION  IN  EIGHT  TEXTS 


TYPE  NUMBER 

TEXT 

1 

2 

3 

4 

5 

6 

7 

8 

Total 

1 

10 

30 

20 

34 

8 

13 

13 

19 

147 

2 

28 

14 

123 

11 

_ 

75 

49 

27 

327 

3 

- 

7 

6 

2 

4 

11 

3 

15 

48 

4 

11 

24 

24 

2 

19 

20 

14 

17 

131 

5 

2 

4 

2 

• 

3 

1 

_ 

1 

13 

6 

5 

10 

4 

9 

3 

13 

4 

52 

100 

7 

_ 

2 

2 

3 

2 

1 

1 

2 

13 

8 

1 

1 

. 

4 

-  . 

4 

1 

- 

11 

9 

2 

7 

3 

- 

1 

1 

2 

12 

28 

10 

- 

1 

13 

2 

2 

13 

3 

2 

36 

11 

6 

19 

13 

3 

« 

4 

11 

16 

72 

12 

1 

• 

2 

- 

1 

1 

3 

- 

8 

13 

- 

1 

1 

2 

4 

1 

• 

1 

10 

14 

9 

42 

12 

41 

3 

14 

39 

30 

190 

15 

- 

12 

5 

- 

1 

- 

18 

4 

40 

16 

1 

2 

1 

1 

1 

8 

1 

8 

23 

17 

6 

1 

1 

1 

- 

2 

2 

- 

13 

18 

8 

- 

4 

- 

1 

- 

3 

7 

23 

19 

9 

- 

3 

1 

- 

- 

1 

1 

15 

Space  does  not  permit  the  reproduction  of  similar  tables  for  addition, 
subtraction,  multiplication  and  the  classes  of  two-step  problems.  In  Table 
XXV  a  summary  of  the  frequencies  of  the  occurrence  of  the  several  types  is 
given.  This  table  is  read  as  follows:  In  the  case  of  problems  requiring  only 
addition,  three  types  occurred  in  all  eight  texts,  one  occurred  in  seven  and  two 
in  six  texts.  The  total  number  of  types  occurring  in  five  or  more  of  the  texts 
is  six.  The  total  number  of  problems  classified  in  these  six  types  is  464.  The 
total  number  of  problems  is  622. 

The  reader  should  bear  in  mind  that  no  attempt  was  made  in  this  classi- 
fication to  determine  what  problems  pupils  should  be  asked  to  solve.  The 


42 

problems  have  been  taken  as  they  occurred  in  the  texts.  In  effecting  the  classi- 
fication, no  consideration  was  given  to  the  question  of  whether  the  problem 
was  practical.  In  fact  the  purpose  was  not  to  obtain  a  list  of  practical  problems 
but  to  secure  a  list  of  the  forms  of  statement  or  language  which  had  been  used 
in  the  one-  and  two-step  problems  by  the  authors  of  widely  used  texts.  Many 
of  the  technical  terms  of  arithmetic  are  used  (probably  must  be  used)  whether 
the  problems  are  practical  or  not. 

Experimental  selection  of  problems.  In  order  to  secure  data  for 
the  construction  of  a  series  of  reasoning  tests  in  arithmetic,  about  300  problems 
were  selected  out  of  the  total  number  examined  and  classified.  Out  of  this  num- 
ber 156  problems  were  chosen  for  an  experimental  series  of  tests.  In  making 
the  selections  for  this  purpose  the  writer  considered,  in  addition  to  the  classifi- 
cation described  above,  the  social  importance  of  the  problems.  Thus  a  few 
types  of  problems  which  occur  in  a  majority  of  the  texts  and  have  a  high  total 
frequency,  were  not  represented.  This  introduces  an  additional  subjective 
factor  but  in  view  of  the  emphasis  which  is  being  placed  upon  the  social  im- 
portance of  the  subject  matter,  the  writer  believes  it  is  better  to  exercise  judg- 
ment in  this  instance  rather  than  to  follow  blindly  statistics  based  upon  the 
content  of  our  present  texts,  particularly  when  it  is  obviously  impossible  to 
include  representative  problems  of  all  types  within  a  single  series  of  tests  of 
suitable  length  for  classroom  use. 


TABLE  XXV.  FREQUENCY  OF  TYPES  OF  PROBLEMS 


NUMBER  OF  TYPES 

OCCURRING   IN 

TOTAL 

FREQUENCY 

FREQUENCY 

OPERATION 

No.  OF 
TYPES 

OF    PROBLEMS 
CLASSIFIED 

OF   ALL 

PROBLEMS 

8 

7 

6 

5 

texts 

texts 

texts 

texts 

+ 

3 

1 

2 

0 

6 

464 

622 

1 

2 

4 

0 

1 

211 

456 

X 

5 

5 

2 

3 

16 

1641 

1938 

-i_ 

5 

6 

3 

5 

19 

1248 

1610 

+  - 

1 

2 

2 

5 

199 

346 

+X 

4 

2 

3 

4 

13 

472 

718 

+-*• 

1 

0 

1 

3 

5 

127 

299 

-X 

0 

0 

1 

1 

8 

166 

559 

;_ 

1 

0 

3 

4 

114 

413 

XX 

3 

1 

2 

4 

10 

429 

581 

x-^ 

1 

4 

2 

6 

13 

704 

1234 

++ 

7 

-S-  -7- 

70 

TOTAL 

25 

23 

25 

32 

105 

5775 

8853 

In  constructing  the  experimental  series,  Test  I  was  designed  for  grades 
four  and  five,  Test  II  for  grades  six  and  seven,  and  Test  III  for  grade  eight. 
Some  such  division  is  necessary  because  certain  social  situations  from  which 


. 


43 

problems  are  taken  are  not  studied  until  the  later  grades  although  the 
mathematical  relationships  are  very  simple.  Pupils  cannot  be  expected  to  solve 
such  problems  until  they  are  acquainted  with  the  social  situations.  For 
this  reason  all  problems  involving  percentage  were  placed  in  Test  III.  No 
consideration  was  given  to  the  relative  difficulty  of  the  problems  in  making 
this  division  except  that  no  problems  requiring  common  fractions  were  placed 
in  Test  I  and  for  the  most  part  decimal  fractions  were  confined  to  Test  III. 

Each  test  consisted  of  sixteen  problems  printed  on  a  four  page  folder 
with  space  so  that  the  pupil  could  do  all  of  his  work  upon  the  test  paper.  The 
test  papers  showed  that  unless  the  pupil  made  errors  and  did  his  work  over  or 
used  an  elaborate  method,  ample  space  was  provided  except  in  a  very  few 
cases.  The  directions  for  administering  the  preliminary  tests  were  essentially 
the  same  as  those  which  now  accompany  the  tests. 

A  number  of  cities  were  invited  to  cooperate  by  giving  the  tests  between 
April  1  and  15,  1918.  Fourteen  cities  responded,  nine  in  Kansas,  and  one 
city  in  each  of  the  following  states:  Illinois,  Ohio,  Michigan,  New  York,  and 
Pennsylvania.  Usable  returns  were  received  from  12,859  pupils. 

When  the  record  sheets  and  the  test  papers  were  returned  to  the  writer 
it  was  found  that  the  directions  for  marking  the  papers  were  not  sufficiently 
complete  and  explicit.  Consequently,  there  was  a  lack  of  uniformity  in  the 
marking.  In  order  to  insure  uniformity  the  writer,  assisted  by  two  clerks 
rescored  the  papers.  Whenever  an  unusual  or  questionable  solution  was 
found  a  record  was  made  and  all  similar  solutions  were  marked  in  the  same  way. 
In  this  way  a  high  degree  of  uniformity  in  the  marking  of  the  papers  was  secured. 
Space  does  not  permit  a  detailed  statement  of  the  plan  of  scoring  of  the  solution 
of  each  problem  but  the  general  plan  may  be  indicated. 

The  solution  of  a  problem  was  considered  correct  in  principle  if  the 
pupil's  work  showed  that  he  had  based  his  solution  upon  the  relationships 
which  exist  between  the  quantities  of  the  problem.  For  example,  in  the 
problem,  "If  a  man  has  $275  in  the  bank  and  draws  out  $70,  how  much  has  he 
left  in  the  bank?",  there  are  three  quantities:  $275,  $70,  and  the  amount 
"left  in  the  bank."  These  are  related  so  that  the  difference  between  $275 
and  $70  must  equal  the  amount  left  in  the  bank.  A  solution  of  the  problem 
based  upon  this  relationship  must  involve  the  subtraction  of  $70  from  $275> 
or  the  finding  of  a  number  which  added  to  $70  will  make  $275. 

In  the  problem,  "A  house  rents  for  $35  a  month.  This  is  how  much  a 
year?",  the  three  quantities  are  $35,  12,  or  the  number  of  months  in  a  year, 
and  the  amount  for  a  year.  The  relation  is  that  the  product  of  $35  and  12 
equals  the  amount  of  rent  for  a  year.  A  solution  based  upon  this  relationship 
would  usually  be  one  in  which  $35  was  multiplied  by  12.  In  a  few  cases  the 
pupil  had  set  down  $35  twelve  times  and  added.  This  solution  was  counted 
as  correct  in  principle  because  it  was  considered  that  the  pupil  had  recognized 


44 

the  relationship  which  existed  between  the  quantities  ot  the  problem.  Inci- 
dentally it  should  be  noted  that  although  such  a  solution  v/as  counted  as  being 
correct  in  scoring  the  papers  of  the  test,  a  teacher  should  not  encourage  it. 
In  fact  the  writer  believes  it  should  be  discouraged,  except  possibly  when  the 
pupil  is  learning  the  idea  of  multiplication,  because  the  method  is  not  efficient. 
It  requires  more  time  and  there  are  more  opportunities  for  error  in  the  mech- 
anical work. 

In  the  case  of  the  above  problem,  if  a  multiplier  other  than  12  was  used  the 
solution  was  counted  as  correct  in  principle  because  it  was  considered  that 
correct  recall  of  denominate  number  facts  was  not  a  part  of  the  reasoning. 
In  a  few  cases  35  was  multiplied  by  itself.  This  was  marked  incorrect  in 
principle. 

Although  the  pupils  were  directed  to  do  all  work  upon  the  test  papers 
a  few  gave  only  the  answer  in  the  case  of  certain  problems.  They  had  either 
solved  the  problem  mentally  or  on  another  sheet  of  paper.  An  arbitrary  rule 
was  adopted.  If  the  answer  was  correct  the  problem  was  marked  correct  in 
principle  and  answer.  If  the  answer  was  wrong  it  was  marked  incorrect  in 
both  principle  and  answer. 

An  answer  was  not  marked  correct  unless  the  solution  of  the  problem 
was  correct  in  principle  and  the  answer  was  numerically  correct  and  in  its 
lowest  terms  if  it  contained  a  fraction.  It  was  not  required  that  the  answer 
be  labeled  with  its  denomination. 

Weighting  the  problems.  For  each  problem  three  records  were  secured : 
(1)  Number  of  pupils  attempting  the  problem.  (2)  Number  of  solutions 
correct  in  principle.  (3)  Number  of  correct  answers.  From  these  facts  the 
percent  of  solutions  correct  in  principle  and  the  percent  of  those  solved  accord- 
ing to  the  right  principle  which  had  also  correct  answers  were  calculated.  These 
percents  were  translated  into  sigma  values.  The  former  being  designated  as 
the  "P"  value  of  the  problem  and  the  latter  as  the  "C"  value.  In  doing  this 
it  was  assumed  that  the  ability  to  solve  problems  was  distributed  normally 
and  included  between  +2.5  sigma  and — 2.5  sigma.  The  tables  given  in  Rugg's 
"Statistical  Methods  as  Applied  to  Education"  were  used.  The  values 
were  calculated  to  two  decimal  places  but  in  order  to  simplify  the  computation 
of  scores  they  were  expressed  in  terms  of  the  nearest  integer  in  the  tests  as  now 
published. 

In  the  case  of  those  problems  which  were  solved  by  the  pupils  in  two 
successive  grades,  the  average  inter-grade  interval  was  found  for  each  group  of 
problems  by  taking  the  average  of  the  differences  of  the  sigma  values  of  the 
problems  of  the  test.  This  inter-grade  interval  was  added  to  the  values  of 
the  problems  for  the  upper  of  the  two  grades  to  reduce  them  to  the  basis  of  the 
lower  grade.  The  average  of  the  two  values  was  taken  as  the  final  value  of 
the  problem. 


45 

An  attempt  was  made  to  reduce  the  sigma  values  to  a  common  zero 
point,  and  thus  secure  comparable  scores,  by  having  a  limited  number  of  prob- 
lems from  Test  I  appear  in  Test  II  and  also  a  limited  number  of  problems  from 
Test  II  appear  in  Test  III.  It  happened  that  some  of  the  problems  chosen 
showed  inversion  and  for  this  reason  it  was  deemed  advisable  not  to  attempt  to 
reduce  the  values  to  a  common  zero.  Thus  the  scores  obtained  from  the  differ- 
ent tests  of  the  series  are  not  comparable.7 

Construction  of  the  final  tests.  Out  of  the  156  problems  included 
in  the  preliminary  test,  90  which  belonged  to  types  occurring  in  five  or  more  of 
the  eight  texts  examined,  were  selected  for  the  final  tests.  Since  in  the  select- 
ion on  the  basis  of  content  there  was  no  effort  to  include  problems  which  ex- 
hibited wide  range  of  difficulty,  there  was  no  attempt  to  construct  a  difficulty 
scale.  In  fact  it  is  the  judgment  of  the  writer  that  the  educational  objectives 
implied  by  such  a  scale  in  the  field  of  problem-solving  are  open  to  serious 
criticism.  In  our  schools  we  should  endeavor  to  instruct  pupils  to  solve 
problems  because  they  are  socially  worth  while  rather  than  because  they  exhibit 
a  certain  degree  of  difficulty.  The  purpose  here  is  to  construct  a  group  of 
tests  containing  problems  that  are  representative  of  the  language  in  which 
problems  are  stated  in  our  representative  text  books  and  which  appear  to  be 
satisfactory  for  testing  purposes. 

The  final  tests  consist  of  15  problems  each.  Test  I  is  for  grades  four 
and  five,  Test  II  for  grades  six  and  seven,  and  Test  III  for  grade  eight.  There 
are  two  forms  of  each  test.  In  selecting  the  90  problems  for  these  tests  those 
were  rejected  which  were  commented  on  unfavorably  by  those  who  gave  the 
preliminary  tests.  Also  those  problems  were  rejected  which  were  found  to  be 
particularly  confusing  to  pupils.  The  arrangement  of  the  order  of  the  problems 
in  a  test  was  made  without  reference  to  their  difficulty  values.  An  attempt 
was  made  to  secure  as  high  degree  of  variation  in  the  operations  required  as. 
possible.  In  the  two  forms  of  each  test  the  corresponding  problems  are  ap- 
proximately equal  in  difficulty,  and  so  far  as  possible,  the  two  forms  were  made 
equivalent  in  other  respects.8 


7The  method  of  weighting  is  open  to  criticism.  It  is  used  in  an  attempt  to  give  more 
credit  for  doing  a  difficult  problem  than  for  doing  an  easy  one.  It  is  not  at  al!  certain  that 
such  a  plan  gives  the  most  truthful  indication  of  a  pupil's  ability.  Some  recent  studies 
have  shown  that  unweighted  scores  correlate  very  highly  with  the  weighted  scores  obtained 
by  this  method.  Therefore,  it  is  likely  that  the  tests  would  have  been  nearly  as  accurate 
measuring  instruments  without  any  determination  of  weights. 

8No  determination  of  the  reliability  or  validity  of  these  tests  was  made  as  a  part  of  the 
original  derivation.  Neither  is  it  possible  to  make  a  report  on  these  questions  at  this  time. 
Some  work  which  was  done  on  the  question  of  reliability  indicated  that  the  tests  were  less 
reliable  than  tests  in  the  operations  of  arithmetic  and  in  silent  reading.  This  appeared  to 
be  due  to  the  fact  that  frequently  pupils  are  unable  to  do  certain  problems  because  of  a 
peculiar  course  of  study. 


46 

Analysis  of  errors  made  by  pupils  on  preliminary  test.  In  the  pre- 
liminary testing  the  following  six  problems  were  given  to  100  fifth  grade 
pupils  in  one  city.  The  results  of  an  analysis  of  the  test  papers  are  given 
in  Table  XXVI. 

1.  Mrs.  Black  received  $2  a  yd.  for  broadcloth.     She  sold  78  yds.     How  much  did  she 
receive  ? 

2.  At  the  store  a  towel  roller  costs  35c.     George  made  one  for  his  mother.     He  used 
12c  worth  of  lumber,  2c  of  hardware,  and  3c  worth  of  shellac.     Find  how  much  George  saved 
his  mother. 

3.  A  Kansas  farmer  bought  80  acres  of  cheap  land  for  $240.    Oil  being  found  on  his 
farm  he  sold  the  land  for  $60,000.     What  was  his  profit? 

4.  A  car  contains  72,060  Ibs.  of  wheat.     How  much  is  it  worth  at  87c  a  bushel? 

5.  A  field  is  20  rds.  long  and  12  rds.  wide.     How  many  rods  of  fence  are  needed  to 
enclose  it? 

6.  What  are  the  average  daily  earnings  of  a  boy  who  received  88  cents,  25  cents,  $1.15, 
75  cents,  50  cents,  and  60  cents  in  one  week? 

TABLE  XXVI.    RESULTS  OF  ANALYZING  THE  ERRORS  OF  100  FIFTH  GRADE 

PUPILS 


PROBLEM 

1 

2 

3 

4 

5 

6 

Total 

Number  of  pupils  attempting 
Errors  in  reasoning 
Errors  in  fundamentals 
Omissions  and  errors  in  copying 
Errors  in  decimals 

100 
8 
1 
2 
13 

100 
21 
7 
0 
0 

92 
39 
26 
2 
16 

52 
38 
16 
3 

25 

94 

33 
2 
0 
0 

94 
67 
35 
4 
14 

532 
206 
87 
11 
68 

Two  significant  facts  are  shown  in  this  table.  First,  a  majority  of  the 
errors  (55  percent)  are  in  reasoning.  More  than  one-third  of  the  attempts 
(39  percent)  resulted  in  faulty  reasoning.  Second,  41  percent  of  the  errors 
in  calculation  were  in  placing  the  decimal  point.  This  second  fact  becomes  more 
significant  when  we  note  that  these  errors  occurred  in  problems  involving  only 
United  States  money  and  that  the  first  and  third  problems  which  produced 
29  of  the  68  errors  do  not  really  involve  decimal  fractions.  In  these  two 
problems  the  error  consisted  in  pointing  off  the  answer  when  it  should  not 
have  been  done. 

The  wide  spread  use  of  the  Courtis  Standard  Research  Tests,  Series  B 
and  other  tests  upon  fundamentals  has  resulted  in  increased  attention  to  the 
fundamental  operations  with  integers.  There  should  be  no  decrease  in  the 
emphasis  upon  this  phase  of  arithmetic  for  one  out  of  six  pupils  made  errors 
in  the  simple  calculations  required  in  these  problems  but  the  greatest  source 
of  error  and  therefore  the  greatest  need  is  increased  attention  to  the  mental 
processes  involved  in  reasoning  as  it  occurs  in  solving  arithmetical  problems. 
The  necessity  for  doing  this  becomes  more  obvious  when  we  examine  the  nature 


47 

of  the  errors  in  reasoning.  In  problem  2,  13  of  the  21  errors  in  reasoning  were 
due  to  adding  all  of  the  terms;  in  problem  4,  33  out  of  38  of  the  errors  in  reason- 
ing were  due  to  multiplying  72,060  by  87  without  attempting  to  reduce  the 
pounds  to  bushels;  in  problem  6,  58  of  the  67  pupils  who  reasoned  incorrectly 
simply  added  the  terms.  Each  of  these  errors  may  be  ascribed  to  inaccurate 
or  incomplete  reading  of  the  problem,  or  the  first  step  in  the  rational  solution 
of  a  problem. 

In  tabulating  the  scores  of  the  preliminary  test  the  variation  in  achieve- 
ment of  different  classes  was  particularly  noticeable.  It  was  evident  that 
some  teachers  were  teaching  their  pupils-  to  solve  problems  while  others,  fre- 
quently within  the  same  school  system,  were  not  doing  so.  It  is  also  sig- 
nificant that  a  number  of  teachers  consistently  marked  as  correct,  solutions 
which  were  clearly  incorrect.  This  may  have  been  accidental  on  the  part  of 
the  teacher  but  this  is  very  doubtful.  A  striking  illustration  was  furnished  by 
the  problem:  "A  baker  used  3/5  Ibs.  of  flour  to  a  loaf  of  bread.  How  many 
loaves  could  he  make  from  a  barrel  (196  Ibs.)  of  flour?"  The  correct  solution 
requires  that  196  be  divided  by  3/5  which  gives  an  answer  of  326  2/3  loaves. 
In  several  instances  teachers  marked  as  correct  all  papers  in  a  class  in  which 
196  was  multiplied  by  3/5.  This  latter  solution  gives  an  answer  of  117  3/5 
loaves.  The  fact  that  teachers  made  such  errors  as  this  indicates  that  they 
are  not  familiar  with  solving  reasoning  problems.  Perhaps  this  is  one  source 
•of  the  poor  records  made  by  the  pupils. 


CHAPTER  IV 

MONROE'S  TIMED  SENTENCE  SPELLING  TESTS  AND  PUPIL'S   ERRORS 

How  ability  in  spelling  should  be  measured.  In  measuring  ability 
in  spelling  by  having  a  pupil  spell  words  which  are  dictated  in  lists  it  is  clear 
that  the  conditions  under  which  the  pupil  spells  the  words  are  not  the  conditions 
under  which  he  spells  the  words  which  he  uses  in  writing  themes,  letters,  and 
other  school  exercises.  As  a  result  we  probably  fail  to  obtain  a  measure  of 
his  "true  spelling  ability." 

-  If  the  test  words  are  embedded  in  sentences  and  the  sentences  written 
from  dictation  we  approach  more  nearly  normal  spelling  conditions  because 
the  pupil  is  writing  connected  words  which  have  meaning.  A  still  closer 
approximation  appears  to  be  secured  by  dictating  the  sentences  at  approx- 
imately the  rate  at  which  the  pupil  is  accustomed  to  write.  By  thus  causing 
the  pupil  to  write  at  approximately  his  normal  rate  of  writing,  he  does  not  have 
time  to  study  over  the  spelling  of  words,  and  as  a  result  we  secure  a  record  of 
spelling  which  is  largely  automatic.  Under  such  conditions  a  pupil 's  attention 
is  centered  primarily  upon  writing  and  not  upon  his  spelling.  Of  course, 
these  conditions  are  not  those  under  which  the  pupil  normally  spells  words. 
The  writing  from  dictation  may  be  an  unusual  exercise  for  the  pupil.  Some 
pupils  will  be  accustomed  to  write  more  slowly  than  the  rate  of  dictation. 
This  may  tend  to  confuse  them.  To  what  extent  these  and  possibly  other 
factors  prevent  our  obtaining  a  record  of  the  "true  spelling  ability"  of  the 
pupil  by  a  timed-dictation  test  we  do  not  know.  It  appears,  however, 
that  a  Timed  Sentence  Spelling  Test  is  likely  to  yield  a  more  valid  measure  of 
spelling  ability  than  a  list  of  words  dictated  separately. 

The  construction  of  Monroe's  Timed  Sentence  Spelling  Tests. 
In  order  to  make  easily  available  a  timed  sentence  spelling  test,  the  writer 
constructed  a  series  of  such  tests,  using  test  words  chosen  from  appropriate 
columns  of  Ayres'  Scale  for  Measuring  the  Ability  in  Spelling  and  basing 
the  rate  of  dictation  upon  the  measurements  of  the  rate  of  handwriting  of  over 
six  thousand  Kansas  school  children.  In  order  that  the  scores  might  have  a 
high  degree  of  reliability  as  measures  of  the  spelling  ability  of  individual 
pupils,  fifty  test  words  were  used  .in  each  test.  According  to  one  study9  the 
probable  error  of  an  individual  score  for  a  test  of  fifty  words  is  less  than  1.00 
when  the  score  is  expressed  as  the  percent  of  words  spelled  correctly.  For  a 
class  of  twenty-five  or  more  pupils  the  probable  error  of  the  class  score  would 
be  0.2. 


is,  A.  S.  "The  reliability  of  spelling  scales  involving  a  'deviation  formula'  for  cor- 
relation." School  and  Society,  4,  (November  11,  1916),  716-22.  This  study  deals  with  the 
reliability  of  tests  consisting  of  isolated  words  and  it  is  possible  that  the  results  might  not 
apply  to  a  timed  sentence  spelling  test. 


49 

For  grades  III  and  IV  the  test  words  were  taken  from  Column  M  of 
Ayres'  Scale  for  Measuring  Ability  in  Spelling.  For  grades  V  and  VI  they 
were  taken  from  Column  Q  and  for  Grades  VII  and  VIII  and  the  high  school 
they  were  taken  from  Coulmans  S,  T,  and  U.  The  test  for  the  fifth  grade  is 
reproduced.  The  sentences  are  to  be  dictated  when  the  second  hand  of  the 
watch  reaches  the  position  indicated  in  the  left-hand  margin. 

In  this  test  no  test  words  come  at  the  end  of  the  sentences.  Thus,  the 
pupil  who  writes  slowly  will  be  much  less  likely  to  make  low  scores  because  he 
does  not  have  time  to  complete  writing  the  sentences.  It  should  also 
be  noted  that  all  other  words  found  in  these  sentences  are  easier  to  spell  as 
shown  by  the  Ayres  Scale.  It  was  thought  advisable  to  allow  time  for  dic- 
tating the  sentences  in  addition  to  the  actual  writing.  For  this  reason,  the 
rate  of  writing  for  each  school  grade  was  increased  by  ten  percent,  sixty-six 
seconds  instead  of  sixty  being  allowed  for  the  number  of  letters  which  pupils 
commonly  write  in  sixty  seconds. 

Tentative  grade  Norms.  This  series  of  timed  sentence  spelling  tests 
was  given  in  sixteen  Kansas  cities  in  April  and  May,  1917.  During  the  school 
year  of  1919-20  scores  were  reported  from  a  number  of  cities.  The  grade  medians 
for  these  two  groups  of  cities  and  the  norms  given  by  Ayres  are  given  in  Table 
XXVII.  In  comparing  the  successive  grades  it  must  be  remembered  that  the 
same  test  words  were  not  used  for  all  grades.  One  list  of  test  words  was  used 
for  grades  III  and  IV,  another  for  grades  V  and  VI  and  still  another  for  grades 
VII  and  VIII  and  for  the  high  school. 

The  fact  that  the  median  scores  in  Table  XXVII  are  materially  below 
Ayres '  norms  indicates  that  a  different  type  of  spelling  ability  has  been  measured 
by  the  timed  spelling  sentence  test  than  that  measured  by  Ayres  in  constucting 
his  scale.  (Ayres  had  the  words  dictated  in  lists).  This  fact  becomes  more 
apparent  when  it  is  recalled  that  many  of  the  cities  which  gave  these  tests 
had  used  Ayres'  Scale  as  a  minimum  course  of  study  as  well  as  a  source  of  test 
words.  Thus,  had  the  test  words  been  dictated  in  lists  it  is  likely  that  the  m 
ian  scores  would  have  been  materially  above  Ayres'  norms.10 

MONROE'S  TIMED  SENTENCE  SPELLING  TEST  ARRANGED  FOR  THE  FIFTH  GRADE. 
Seconds 

60  The  president  gave  important  information  to  the  men. 

48  The  women  were  present  at  the  time. 
19  The  entire  region  was  burned  over. 

49  The  gentlemen  declare  the  result  was  printed. 
30  Suppose  a  special  attempt  is  made. 


10It  is  possible  that  the  difference  between  the  median  scores  and  Ayres 'norms  may  be 
due  to  factors  other  than  the  measurement  of  different  types  of  spelling  ability.  Many  of 
the  pupils  probably  were  not  accustomed  to  writing  from  dictation  and  all  were  not  accustomed 
to  writing  at  the  rate  at  which  these  tests  were  dictated.  It  is  possible  that  these  unusual 
conditions  may  have  been  operated  to  materially  lower  the  scores  of  a  number  of  pupils 
or  even  of  most  pupils. 


50 


60  The  final  debates  were  held. 
24  Tht  factory  employs  forty  men. 

51  Sometimes  the  connection  is  not  made. 

24  I  enclose  a  written  statement  with  the  book. 
3  Prompt  action  is  needed. 

25  It  was  a  wonderful  surprise  to  all. 

55  The  addition  to  the  property  was  begun. 

31  Remember \  Saturday  is  the 'day. 

57  They  await  their  leader. 

19  Either  make  another  ^or/  or  return. 

52  The  famous  estate  is  close. 

16  In  this  section  little  progress  was  made. 

53  The  measure  is  */#£  to  pass. 
16  A  position  in  the  field  is  his. 

42  To  o>^0 w  was  the  command  given  ? 

8  Whose  claim  was  bought? 
29  He  represents  the  firm  in  this  matter. 

2  Go  forward  in  that  direction  to  reach  the  city. 


When  the  second  hand  reaches  43,  stop  the  writing. 

Allow  no  corrections  or  additions  to  be  made.     Ask  the  pupils  to  turn  their  papers  over 
and  write  their  name  and  grade.     Appoint  two  or  three  pupils  to  collect  the  papers. 


TABLE  XXVII.    MEDIAN  SCORES  (WORDS  SPELLED  CORRECTLY)  AND 
AYRES '  NORMS.    TOTAL  WORDS  IN  EACH  TEST  IS  FIFTY 


GRADE 


ni 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

1917  TESTING 
Number  of  pupils 
Median  (May) 
1919-20  TESTING 
Number  of  pupils 
Median 
Ayres  Norms 

1342 
28.6 

437 
28.2 
33.0 

1539 
39.4 

423 
43.0 
42.0 

1427 
32.8 

440 
39.7 
36.5 

1338 
41.8 

302 
43.0 
42.0 

1136 

35.1 

218 
32.6 
39.0 

876 
43.0 

153 
38.8 
44.0 

289 
43.3 

251 
45.1 

188 
46.5 

96 
47.9 

In  Table  XXVIII  the  distributions  of  the  scores  are  given  for  grades 
III  to  VIII  inclusive.  In  the  fourth,  sixth,  and  eighth  grades  there  are  a 
number  of  perfect  scores  which  show  that  the  test  was  not  sufficiently  difficult 
for  the  best  spellers  in  these  grades  and,  therefore,  did  not  give  us  a  measure 
of  their  spelling  ability.  This  statement  probably  applies  also  to  those  pupils 
who  spelled  incorrectly  one,  two,  or  three  words.  From  the  standpoint  of 
accurate  measurement  of  the  spelling  ability  of  "good  spellers/'  these  tests 
are  too  easy,  especially  for  grades  four,  six,  and  eight  and  the  high  school. 

This  table  is  also  significant  in  another  respect.  The  range  in  the  number 
of  words  spelled  correctly  extends  from  zero,  or  at  the  most  two,  up  to  fifty 
and,  as  has  been  pointed  out  in  the  above  paragraph,  the  spelling  ability  of 
some  pupils  probably  extends  beyond  perfect  scores  on  these  tests.  That  the 


51 


TABLE  XXVIII.     DISTRIBUTION  OF  SPELLING 

SCORES  ON  MONROE'S  TIMED  SENTENCE 

SPELLING  TESTS 


GRADE 

III 

IV 

V 

VI 

VII 

VIII 

50 

7 

45 

13 

40 

14 

33 

49 

11 

53 

23 

83 

21 

48 

48 

13 

82 

29 

75 

31 

64 

47 

17 

76 

44 

81 

45 

60 

46 

24 

83 

30 

82 

40 

55 

45 

28 

89 

38 

77 

38 

61 

44 

17 

63 

50 

78 

39 

59 

43 

34 

64 

38 

81 

54 

59 

42 

36 

58 

49 

60 

34 

48 

41 

37 

45 

49 

62 

30 

40 

40 

35 

76 

55 

69 

37 

33 

39 

39 

57 

31 

47 

40 

25 

38 

29 

67 

35 

48 

34 

29 

37 

30 

42 

55 

43 

30 

28 

36 

43 

53 

44 

34 

44 

17 

35 

45 

43 

42 

38 

40 

25 

34 

43 

52 

41 

23 

29 

22 

33 

27 

36 

40 

32 

40 

18 

32 

30 

43 

46 

20 

31 

19 

31 

42 

30 

40 

24 

41 

12 

30 

35 

33 

46 

33 

29 

24 

29 

35 

33 

41 

16 

23 

13 

28 

31 

34 

35 

17 

23 

12 

27 

32 

44 

29 

16 

23 

10 

26 

30 

23 

40 

13 

28 

7 

25 

34 

16 

39 

18 

32 

14 

24 

37 

23 

42 

9 

23 

3 

23 

38 

26 

27 

15 

13 

10 

22 

26 

19 

16 

3 

27 

5 

21 

30 

21 

30 

13 

14 

5 

20 

39 

10 

25 

11 

18 

4 

19 

23 

9 

21 

5 

24 

4 

18 

22 

6 

24 

7 

14 

1 

17 

21 

6 

16 

9 

18 

2 

16 

30 

9 

18 

9 

21 

1 

15 

24 

13 

22 

6 

20 

14 

26 

8 

17 

7 

10 

1 

13 

23 

8 

14 

5 

7 

2 

12 

21 

5 

18 

5 

10 

11 

22 

2 

15 

4 

8 

1 

10 

23 

8 

9 

2 

8 

9 

23 

6 

16 

4 

5 

8 

25 

1 

9 

2 

4 

7 

18 

2 

10 

3 

5 

1 

6 

12 

3 

7 

1 

2 

5 

10 

6 

3 

6 

4 

16 

12 

2 

3 

11 

4 

11 

2 

4 

2 

11 

4 

6 

2 

1 

1 

1 

12 

3 

10 

1 

1 

0 

15 

3 

4 

1 

Total 

1342 

1539 

1427 

1338 

1136 

876 

Median 

28.6 

39.4 

32.8 

41.8 

35.1 

43.0 

52 

pupils  of  a  grade  exhibit  a  wide  range  of  ability  is  a  well  known  fact.  We 
also  know  that  there  is  a  very  large  degree  of  over-lapping  between  successive 
grades.  Probably  all  would  admit  that  a  grouping  of  pupils  for  purposes 
of  instruction  exhibiting  such  great  differences  in  spelling  ability  does  not  make 
for  the  most  effective  instruction.  Correction  of  this  condition  is  sometimes 
difficult.  In  ungraded  schools  or  in  rooms  where  there  are  two  or  more  grades, 
it  is  relatively  easy  to  group  the  children  for  spelling  instruction,  but  in  rooms 
Where  all  the  pupils  belong  to  the  same  grade  this  is  more  difficult.  The 
pupils  who  make  perfect  scores  or  scores  nearly  perfect  might  be  excused  from 
spelling  but  this  would  not  take  care  of  those  most  needing  instruction. 

In  view  of  the  fact  that  the  time  devoted  to  spelling  is  more  frequently 
used  in  testing  spelling  than  in  teaching  spelling,  this  table  suggests  that  there 
is  a  definite  need  for  teaching  some  pupils  to  spell.  Some  pupils  appear  to  have 
learned  to  spell  under  the  type  of  "  instruction  "  which  the  schools  now  provide, 
but  a  large  number  of  pupils  have  not  done  so.  These  pupils  require  a  different 
type  of  "instruction."  They  probably  need  some  assistance  in  learning  to 
spell. 

Spelling  errors.  In  the  1917  testing,  several  cities  returned,  in  addition 
to  the  class  record  sheets  on  which  were  recorded  the  scores,  the  test  papers. 
The  specific  errors  in  spelling  the  test  words  have  been  carefully  tabulated  for 
430  third  grade  pupils,  463  fourth  grade  pupils,  294  fifth  grade  pupils,  188 
ninth  grade  pupils,  120  tenth  grade  pupils,  107  eleventh  grade  pupils,  and  169 
twelfth  grade  pupils.  This  study  of  errors  was  not  extended  as  originally 
planned  to  the  pupils  in  the  sixth,  seventh,  and  eighth  grades  because  of  a  lack 
of  funds. 

The  fundamental  reason  for  giving  tests  is  to  secure  information  concern- 
ing the  abilities  of  pupils.  In  order  that  this  information  may  be  most  helpful 
to  us  it  is  necessary  that  we  interpret  the  scores  in  terms  of  pupil  needs.  The 
fact  that  a  pupil  has  a  certain  score  and  that  this  score  is  above  standard  or 
below  standard  becomes  significant  to  the  teacher  only  when  this  fact  is  ex- 
pressed in  terms  of  the  learning  needs  of  this  pupil.  In  the  case  of  scores 
below  standards  we  have  only  partially  interpreted  them  when  we  say  that  the 
pupils  having  such  scores  need  to  place  more  emphasis  upon  their  spelling  or 
that  they  need  assistance  from  the  teacher.  We  carry  the  interpretation  a 
step  further  when  we  specify  what  words  the  pupils  need  to  give  their  attention 
to.  We  may  carry  our  interpretation  another  step  by  ascertaining  the  par- 
ticular errors  which  the  pupils  are  making  and  hence  need  to  correct. 

The  tabulations  of  the  misspellings  show  that  some  ways  of  misspelling 
a  word  occur  much  more  frequently  than  others.  In  general  about  60  percent 
of  the  misspellings  belong  to  one  of  five  kinds  and  about  30  percent  are  included 
in  one.  If  a  teacher  knows  the  types  of  misspellings  which  are  most  likely  to 


53 


TABLE  XXIX.    THE  FREQUENCY  OF  MISSPELLINGS  OF  THE  WORDS 

"COLLECT"  AND  "OMIT"  AS  FOUND  IN  THE  TEST  PAPERS 

463    FOURTH    GRADE    PUPILS.    WHERE    NO 

FREQUENCY     IS     GIVEN     THE     MIS- 

SPELLING  OCCURRED  ONLY  ONCE. 

Collect  Omit 


colect 

110 

culate 

omite 

35 

poment 

elect 

21 

cucket 

oment 

22 

phone 

deck 

9 

colest 

omet 

19 

omoit 

clet 

5 

connect 

omitt 

10 

amint 

celect 

4 

cluck 

omeat 

10 

only  me 

clack 

4 

polet 

ommit 

8 

eneat 

docket 

3 

coiker 

omitte 

6 

anete 

colcet 

3 

cluct 

onit 

5 

enit 

cloct 

3 

coulack 

ownit 

5 

bremet 

cleat 

3 

cleick 

admit 

5 

obeat 

cluk 

3 

clach 

omnit 

3 

ument 

colet 

2 

clacket 

ament 

3 

opit 

col 

2 

klechit 

omnitt 

3 

omett 

collet 

2 

clich 

omt 

2 

oumient 

coloct 

2 

clank 

amit 

2 

omemt 

corlect 

2 

klocet 

ameit 

2 

portment 

cllect 

2 

klucklect 

amite 

2 

owmet 

clock 

2 

clouct 

ornate 

2 

oneit 

culect 

2 

colict 

omeet 

2 

omant 

cocet 

2 

colcailate 

only 

2 

owe  meat 

comelet 

clloe 

onipe 

connect 

ceaclect 

caluct 

omot 

obment 

calect 

clearty 

amite 

pomit 

somelet 

coloce 

omiet 

onitt 

golet 
klited 

colack 
claxt 

poemet 
omitted 

nent 
inate 

dontlet 

conckle 

onight 

oak 

kleke 

conut 

anitt 

onight 

kolicket 

coulet 

abment 

own 

cleakely 

collice 

onet 

cault 

clecet 

comen 

celec 

colcect 

onent 

clecty 

cacated 

emmit 

codec  t 

cleclect 

amited 

colext 

clucker 

otamate 

collete 

clecket 

offit 

clllect 

cleack 

adnet 

collecks 

colucket 

aneat 

clete 

concect 

anint 

cole 

cart 

omoitte 

cleatlet 
cherd 

lecke 
coul 

opote 
ohmit 

colectt 

coleck 

omote 

cocllict 

obed 

kalat 

omip 

clectket 

amet 

cleakit 

tell  me 

coluct 

anpend 

occur  she  can,  in  her  teaching  of  spelling,  warn  pupils  against  the  errors  which 
they  will  most  likely  make  and  give  them  such  training  as  may  be  required  to 
insure  that  they  will  not  make  these  errors. 

Because  of  the  importance  of  giving  attention  to  spelling  errors,  we  give 
in  Table  XXIX  the  various  misspellings  of  the  words  "collect"  and  "omit" 


54 


found  in  the  examination  of  463  fourth  grade  test  papers.  Some  of  the  mis- 
spellings which  occur  only  once  or  at  the  most  two  or  three  times  probably 
should  not  be  counted  as  "true"  misspellings.  The  writing  of  c-o-1  probably 
should  be  counted  as  an  incomplete  spelling.  The  writing  of  c-h-e-r-d  indicates 
either  that  the  pupil  is  not  acquainted  with  the  word  "collect"  or  was  unable 
to  recall  automatically  the  spelling,  or  failed  to  understand  the  word  in  the 
teacher's  dictation.  On  the  other  hand  the  misspellings  which  recur  frequently 
may  be  considered  as  "true"  misspellings  and  are  the  ones  which  should  be 
guarded  against  in  the  teaching  of  spelling. 

In  interpreting  spelling  scores,  we  need  to  consider  the  questions, 
"Are  all  misspellings  to  be  treated  alike?     Does  one  misspelling  mean  the  same 

TABLE  XXX.     SHOWING  MOST  FREQUENT  MISSPELLINGS  OF  THE  TEST  WORDS 
IN  GRADE  III  BY  430  PUPILS 


CORRECT  FORM 

NO.  OF  MIS- 

FIVE MOST  FREQUENT  MISSPELLINGS 

OF 

SPELLINGS 

WORD 

1 

2 

3 

4 

5 

account 

218 

acount 

63 

count 

46 

ocount 

1C 

mony 

8 

accont 

again 

177 

agin 

52 

agan 

40 

agen 

30 

agian 

14 

agun 

almost 

157 

allmost 

101 

alnost 

13 

allnost 

12 

allmast 

3 

amost 

anyway 

105 

enyway 

27 

eneyway 

Y 

inway 

5 

annyway 

4 

inyway 

army 
begin 
begun 
beside 

115 
169 
196 
89 

armey 
began 
began 
by 

li< 
48 
49 
29 

arny 
begain 
begin 
besid 

15 
36 
37 
20 

arme 
begun 
begain 
becide 

15 
22 
30 

armer 
begen 
begone 
besaid 

5 

16 
9 
3 

armay 
begine 
begon 
besied 

both 

72 

those 

21 

bout 

6 

bothe 

3 

boath 

3 

bot 

bought 
change 
children 

185 
165 
135 

bot 
chang 
childern 

85 
23 
25 

bout 
changs 
childen 

19 

14 
12 

brought 
chain 
chirdlren 

13 
11 

5 

bough 
chanes 
childred 

11 
10 
5 

boght 
chanse 
childer 

collect 

219 

colect 

36 

elect 

26 

clact 

4 

clet 

4 

olaolr 

contract 

172 

contrack 

49 

contrach 

5 

contrect 

4 

contracked  4 

ciacK 

deal 

167 

deel 

45 

dill 

28 

dell 

27 

dile 

17 

del 

died 

120 

dide 

50 

did 

If 

dided 

13 

dead 

7 

dress 

55 

drees 

12 

dreess 

8 

drass 

8 

dres 

2 

, 

drill 

69 

dril 

21 

drell 

7 

dill 

g 

grill 

4 

drail 

driven 

77 

drive 

11 

driving 

5 

dreven 

r 

drivin 

5 

enter 

159 

inter 

71 

anter 

13 

enture 

7 

intre 

4 

ender 

extra 

174 

extry 

3i 

exter 

10 

antra 

5 

extery 

4 

extray 

few 

134 

you 

48 

fue 

32 

to 

8 

flew 

6 

do 

follow 

123 

folow 

14 

foller 

8 

fallow 

7 

folio 

6 

flow 

goes 

162 

gose 

4t 

gos 

47 

go 

44 

goese 

2 

nrnp 

great 

188 

grate 

91 

grat 

33 

graet 

10 

grait 

8 

Kue 

grad 

income 

140 

incom 

12 

mcone 

8 

come 

5 

en  come 

2 

fel  W\J 

inform 

107 

inforn 

17 

reform 

12 

infrom 

9 

imform 

6 

incume 

members 

122 

menbers 

IS 

meners 

9 

mambers 

8 

mebers 

5 

mimbers 

might 

155 

mite 

75 

mit 

24 

mint 

11 

night 

5 

mighe 

money 

126 

mony 

63 

many 

9 

maney 

8 

noney 

3 

momy 

month 

149 

mounth 

42 

moth 

30 

mouth 

17 

mount 

9 

office 

138 

ofice 

23 

offic 

21 

offes 

16 

offer 

8 

ofis 

omit 

188 

omet 

25 

omite 

21 

oment 

15 

onit 

14 

omeat 

paid 

167 

pade 

51 

payed 

32 

pad 

28 

pay 

18 

payd 

past 
picture 
please 
provide 
railroad 

119 
131 
165 
128 
111 

passed 
pitcher 
pleas 
provied 
railrode 

30 

17 
77 
10 
12 

pass 
picher 
plese 
provid 
rayroad 

22 

13 

17 

8 
7 

pas 
pictur 
pies 
proved 
ralroad 

9 
9 

8 
8 
4 

pasted 
pictors 
pleace 
proveid 
railroat 

7 
7 
7 
7 
3 

pask 
pctcure 
place 
prove 
roilroad 

ready 

144 

redy 

3(' 

rady 

22 

read 

9 

redey 

7 

rade 

recover 

120 

cover 

22 

uncover 

20 

recove 

£ 

recuver 

8 

recome 

return 

98 

reture 

1?, 

returne 

7 

retun 

5 

returne 

4 

retern 

says 

138 

sais 

ir 

said 

17 

say 

13 

saids 

10 

those 

140 

thoes 

76 

thos 

14 

thouse 

fi 

thous 

5 

thoses 

ticket 

69 

tick 

IS 

ticked 

5 

tickit 

5 

ticke 

3 

tecket 

took 

88 

tuck 

16 

tock   , 

13 

take 

7 

tooke 

5 

tuk 

unable 

82 

unabel 

10 

onabel 

6 

unabil 

5 

unble 

5 

onable 

understand 

83 

unstand 

13 

under 

5 

understant 

5 

undestand 

4 

understend 

while 

109 

whil 

22 

wile 

21 

whill 

11 

will 

10 

whv 

who 

124 

how 

48 

ho 

35 

hoe 

8 

hew 

6 

wuy 

hoo 

TOTAL 

6743 

1845 

903 

544 

331 

2! 

PERCENT 

27 

13 

8 

5 

55 


as  any  other  misspelling?"  Does  "colect"  have  the  same  meaning  with  refer- 
ence to  the  pupil's  need  for  instruction  as  "connect"  or  "cole"  or  "ceaclect?" 
Probably  all  misspellings  do  not  indicate  the  same  instructional  needs.  The 
writing  of  "colect,"  as  was  done  by  nearly  one-fourth  of  all  these  fourth 
grade  pupils,  indicates  uncertainty  concerning  the  double  consonant  or  a 
wrong  habit  formed.  "Connect"  probably  indicates  that  the  word  was 
misunderstood.  "Ceaclect"  indicates  the  lack  of  a  fixed  habit  and  possibly 
that  the  pupil  was  not  acquainted  with  the  word. 

In  Tables  XXX,  XXXI,  and  XXXII,  we  give  a  list  of  the  five  most 
frequent  misspellings11  of  the  test  words  in  grades  III,  IV  and  V.    The  column 

TABLE  XXXI.     THE  MOST  FREQUENT  MISSPELLINGS  OF  THE  TEST  WORDS  IN 
GRADE  IV  BY  463  PUPILS 


CORRECT  FORM 

OF 

WORD 

NO.  OF  MIS- 
SPELLINGS 

FlVEMOST  FREQUENT  MISSPELLINGS 

1 

2 

3 

4 

5 

account 

246 

acount 

104 

count 

42 

ocount 

12 

accont 

7 

acont 

again 

101 

agin 

40 

agan 

27 

agian 

I- 

agen 

g 

agine 

almost 

136 

allmost 

H;; 

alnost 

28 

most 

3 

ainose 

2 

almos 

anyway 

76 

enyway 

2: 

eneyway 

7 

any 

6 

inyway 

Q 

anway 

army 

78 

armey 

17 

arny 

I 

arm 

7 

arme 

4 

arney 

begin 

137 

began 

52 

begain 

33 

begen 

10 

begun 

< 

begon 

begun 
beside 

200 
55 

began 
besid 

51 

21 

begin 
by 

33 
9 

begain 
becide 

21 
5 

begon 
besde 

1C 
2 

becine 
aside 

both 

77 

bouth 

16 

those 

14 

bough 

10 

bothe 

e 

bought 

change 
children 

144 
63 

chang 
chirldren 

21 
11 

changes 
childern 

11 
6 

changed 
chirlden 

8 
5 

chanes 
chrildren 

fc 

4 

chane 
chidera 

collect 

257 

colect 

110 

elect 

21 

deck 

G 

clet 

5 

celect 

contract 

178 

contrack 

4P 

comtract 

25 

contrat 

8 

concrat 

7 

contrach 

deal 

106 

deel 

26 

dell 

24 

del 

6 

dill 

6 

dile 

died 

72 

dide 

2f. 

die 

£ 

dided 

6 

did 

6 

Died 

dress 

31 

drees 

7 

dreess 

3 

dres 

3 

Dress 

2 

drese 

drill 

59 

dril 

1C 

drell 

7 

dill 

4 

trill 

3 

Drill 

driven 

66 

drivin 

1 

dreven 

4 

drive 

3 

drivvin 

8 

driver 

enter 

99 

inter 

61 

en  ten 

3 

entere 

8 

anter 

a 

ender 

extra 

159 

extry 

45 

extray 

8 

extery 

6 

exter 

5 

axtra 

few 

132 

you 

56 

fue 

32 

fiew 

6 

tue 

3 

fhew 

follow 

97 

fallow 

19 

flow 

11 

folow 

10 

fllow 

6 

foller 

goes 

88 

go 

34 

gose 

30 

gos 

17 

gois 

2 

was 

great 

95 

grate 

62 

geart 

5 

grat 

4 

greate 

4 

gred 

income 

90 

incone 

1? 

incom 

16 

encome 

7 

incon 

4 

icome 

inform 

132 

inforn 

38 

imform 

16 

informe 

13 

enform 

7 

enforn 

members 

129 

menbers 

31 

members 

7 

memers 

6 

meners 

5 

membes 

might 

121 

mite 

57 

mit 

14 

mint 

14 

migh 

5 

night 

money 

79 

mony 

4C 

noney 

7 

nony 

2 

momey 

2 

moeny 

month 

114 

mounth 

31 

mouth 

18 

nounth 

11 

moth 

8 

mount 

office 

94 

ofice 

20 

ofic 

15 

offic 

6 

offer 

C 

offece 

omit 

205 

omite 

3~. 

oment 

22 

omet 

It 

omitt 

10 

omeat 

paid 

103 

payed 

M 

pade 

15 

pad 

12 

paied 

6 

Paid 

past 
picture 

69 
75 

passed 
pitcher 

2;" 
U 

pass 
pitcure 

18 
10 

Picture 

5 
8 

pasted 
pictur 

4 

pass 
pictor 

please 

121 

pleas 

6f 

plese 

14 

plase 

5 

plise 

5 

pleace 

provide 
railroad 

160 
73 

provied 
railrode 

1C' 
21 

provid 
ralrode 

12 
3 

pervide 
railrad 

8 
3 

proved 
roilroad 

2 

porvide 
Rail  Road 

ready 

78 

redy 

27 

rady 

H 

reddy 

6 

read 

8 

raid 

recover 

118 

cover 

40 

uncover 

17 

recove 

12 

recuver 

f 

rn  cover 

return 

62 

returne 

11 

retun 

8 

retern 

8 

retrun 

4 

retune 

says 

105 

said 

24 

sais 

IP 

say 

4 

ses 

t 

saids 

those 

96 

thoes 

58 

thos 

10 

thouse 

4 

thoese 

3 

thoses 

ticket 

46 

tick 

c 

tichet 

5 

ticet 

3 

tictect 

2 

tickt 

took 

47 

tuck 

1C 

tock 

8 

toke 

7 

tuke 

2 

take 

unable 

73 

anable 

If 

onable 

8 

unabel 

5 

inable 

5 

uable 

understand 

61 

unstand 

13 

understad 

5 

undersand 

4 

understan 

T 

undestand 

while 

61 

whil 

16 

will 

8 

whill 

7 

wile 

5 

whal 

who 

69 

how 

26 

ho 

22 

Hew 

5 

wow 

3 

whow 

TOTAL 

5133 

1683 

714 

388 

236 

1 

PER  CENT 

33 

14 

1 

5 

56 


headed  "number  of  misspellings"  gives  the  total  number  of  misspellings. 
In  the  following  columns  the  five  most  frequent  misspellings  are  given  with 
their  frequencies. 

The  column  giving  the  total  number  of  misspellings  shows  clearly  that 
these  words  were  not  equal  in  difficulty  for  these  pupils,  although  they  were 
taken  from  the  same  columns  of  Ayres '  Scale.  This  condition  indicates  a 
limitation  of  that  scale.  This  may  be  due  to  the  fact  that  in  deriving  the  scale 
Ayres  used  scores  from  many  different  states  and  hence  the  evaluation  of  the 
words  was  more  general.  It  may  also  be  due  to  the  use  of  the  scale  as  a  mini- 
mum essential  list.  A  third  reason  may  be  the  nature  of  the  test  which  was 
used. 

TABLE  XXXII.     THE  MOST  FREQUENT  MISSPELLINGS  OF  TEST  WORDS  IN  GRADE  V, 

BY  294  PUPILS 


CORRECT  FORM 

No.  OF 

FIVE  MOST  FREQUENT  MISSPELLINGS 

OF 
WORD 

misspellings 

1 

2 

3 

4 

5 

action 

35 

actin 

3 

acionn 

3 

axion 

1 

actshon 

l 

axchian 

1 

addition 

127 

addion 

24 

adition 

21 

addation 

8 

addtion 

fe 

additon 

8 

attempt 

144 

atempt 

34 

attemp 

12 

attenpt 

11 

etempt 

6 

atemp 

6 

await 

136 

awake 

62 

awate 

18 

awaked 

U 

wait 

b 

awaite 

4 

claim 

145 

clame 

79 

plain 

12 

clam 

12 

clain 

11 

claime 

6 

command 

111 

comand 

62 

comman 

commend 

commad 

4 

comend 

4 

connection 

95 

conection 

47 

conecton 

4 

coniction 

conections 

2 

connect 

2 

declare 

152 

declared 

65 

declair 

17 

declaired 

declar 

6 

declard 

& 

due 

78 

dew 

35 

do 

doe 

du 

o 

doo 

2 

effort 

122 

effert 

28 

efert 

21 

efort 

15 

effer 

6 

effor 

5 

Either 

155 

Eather 

99 

Ether 

20 

Eathe 

either 

2 

Eaither 

2 

employs 

178 

imploys 

43 

employes 

17 

inploys 

1 

imployes 

10 

employ 

T 

entire 

123 

intire 

80 

inter 

7 

intier 

intiar 

2 

intre 

2 

estate 

99 

astate 

41 

state 

23 

asstate 

estait 

2 

states 

2 

direction 

84 

dirrection 

14 

drection 

10 

way 

derection 

driction 

3 

famous 

109 

famious 

27 

famis 

10 

famos 

fames 

r 

famest 

5 

field 

33 

feild 

22 

fields 

2 

feeld 

feilds 

1 

fieled 

1 

firm 

69 

ferm 

17 

firn 

11 

furm 

fern 

s 

form 

3 

forward 

74 

foward 

28 

foreward 

14 

frward 

fored 

1 

forwar 

1 

factory 

72 

factor 

13 

facture 

8 

factry 

fatory 

factiory 

3 

final 

88 

finel 

34 

finial 

11 

finally 

lineal 

3 

finall 

3 

gentlemen 
important 
information 

113 
117 
129 

gentleman 
importent 
information 

41 
18 
32 

Gentlemen 
inportant 
infermatioi 

9 

7 
i  7 

gentle 
inportent 
message 

gentlmen 
importanc 
imfermatic 

4 
6 
n5 

gentlenen 
imporant 
infomation 

a 

6 
3 

measure 

55 

masure 

24 

mesure 

3 

maisure 

meashure 

1 

maisure 

1 

present 

57 

presant 

13 

preasant 

3 

preasent 

3 

prisent 

2 

presint 

2 

president 

131 

President 

33 

presedent 

9 

Presdent 

6 

Presedent 

4 

presedient 

3 

Prompt 

123 

Promp 

40 

prompt 

13 

Promt 

7 

Promped 

6 

pronpt 

4 

property 

89 

propty 

24 

proptery 

9 

propity 

6 

propety 

5 

propery 

4 

progress 

101 

progus 

9 

progess 

8 

progres 

8 

pro  grass 

5 

progrees 

3 

position 

289 

possion 

42 

postion 

34 

posion 

25 

physician 

S 

possition 

7 

region 

137 

regin 

20 

regon 

20 

reigon 

12 

reagon 

12 

regen 

7 

Remember 

156 

Rember 

93 

rember 

12 

Remeber 

8 

Remmber 

6 

remember 

4 

represents 

132 

repesents 

16 

repersents 

13 

represent 

13 

repersent 

4 

reperzents 

3 

result 

30 

rezult 

4 

reselt 

3 

ruselt 

2 

resuled 

2 

it 

2 

Saturday 

123 

Saturday 

37 

Saterday 

27 

Sat. 

5 

Saturdy 

5 

Satuarday 

5 

section 

54 

sextion 

9 

secton 

6 

sexion 

2 

sexton 

2 

Section 

1 

statement 

97 

statment 

41 

stament 

5 

statemet 

4 

satment 

3 

statemen 

3 

special 

104 

specil 

11 

specal 

11 

spechal 

3 

speshel 

3 

speacle 

3 

Suppose 

188 

Supose 

67 

suppose 

56 

Sopose 

U; 

Soppose 

S 

supose 

3 

surprise 

183 

suprise        103 

supprise 

26 

suprize 

7 

surprize 

6 

supprize 

3 

Sometimes 

46 

Sometine 

13 

Sometines 

6 

Sometine 

5 

Sometime 

3 

Sontimes 

3 

whom 

96 

shome 

17 

horn 

14 

home 

13 

who 

9 

hoom 

9 

Whose 

127 

Whos 

31 

She's 

23 

Who 

21 

Whoes 

16 

whos 

7 

women 

83 

wemon 

24 

wemen 

13 

woman 

11 

weman 

10 

wimen 

4 

wonderful 

86 

wounderful 

23 

wonder 

8 

wondful 

8 

woundful 

15 

wonderfull 

5 

TOTAL 

5075 

1642 

619 

346 

239 

173 

PER  CENT 

32 

12 

7 

5 

3 

"This  includes  in  certain  cases,  the  wrong  use  of  the  capital  letter.  A  test  word  be- 
ginning a  sentence  was  counted  wrong  if  not  capitalized.  A  test  word  which  should  be 
begun  with  a  capital  letter  was  counted  wrong  if  the  pupil  failed  to  do  this. 


57 


APPENDIX 

In  the  following  tables,  5, 10,20  30,40,  50,  60,  70,  80,  90  and  95  percentile  scores  are 
given  for  several  tests.  In  general  these  are  tests  which  have  been  widely  used  and  which 
appear  to  have  some  permanence.  The  interpretation  of  a  percentile  score  is  similiar  to 
that  of  a  median.  In  fact  the  50-percentile  score  is  the  median.  The  20-percentile  score  is 
the  score  above  which  there  are  eighty  percent  of  the  scores  and  below  which  there  are 
twenty  per  cent.  These  tables  are  to  be  used  for  determining  the  position  which  a  pupil 
occupies  in  the  total  distribution  of  his  grade. 

TABLE  I.    MONROE'S  STANDARDIZED  REASONING  TESTS  IN  ARITHMETIC 
FORM  I.     PERCENTILE  SCORES  BASED  ON  APRIL  TESTING 

CORRECT  ANSWER 


GRADE 

Percentile 

IV 

V 

VI 

VII 

VIII 

95 

16.5 

21.1 

20.0 

23.5 

18.4 

90 

14.4 

19.1 

17.8 

21.2 

16.5 

80 

11.7 

16.5 

14.9 

18.5 

14.0 

70 

9.9 

14.7 

13.2 

16.5 

12.1 

60 

8.4 

13.0 

11.7 

14.9 

10.4 

50 

7.0 

11.3 

10.4 

13.4 

9.0 

40 

5.9 

9.7 

9.0 

11.9 

7.5 

30 

4.7 

8.0 

7.6 

10.4 

5.9 

20 

3.5 

6.2 

6.0 

8.5 

4.2 

10 

2.0 

4.0 

4.0 

6.0 

2.4 

5 

1.1 

2.4 

2.8 

4.0 

1.4 

No.  of 

pupils 

2968 

2996 

3518 

2803 

2515 

CORRECT  PRINCIPLE 


95 

26.7 

33.8 

26.5 

28.9 

29.6 

90 

23.0 

31.5 

23.8 

27.9 

26.6 

80 

18.5 

27.5 

20.7 

25.5 

24.0 

70 

15.6 

25.7 

18.2 

23.2 

21.8 

60 

13.3 

22.2 

16.0 

21.4 

19.5 

50 

11.3 

19.2 

14.2 

19.7 

17.2 

40 

9.2 

16.4 

12.7 

17.7 

15.1 

30 

7.2 

13.7 

11.1 

15.4 

12.7 

20 

5.2 

10.3 

9.2 

13.0 

9.9 

10 

2.8 

6.4 

6.6 

9.9 

6.4 

5 

1.1 

3.9 

4.7 

7.5 

4.1 

No.  of 

pupils 

2932 

3027 

3498 

2706 

2472 

RATE 


95 

16.4 

23.4 

18.1 

20.4 

17.3 

90 

14.5 

19.5 

15.5 

18.3 

14.9 

80 

11.8 

15.9 

12.9 

15.4 

12.0 

70 

10.0 

14.0 

11.4 

13.7 

10.1 

60 

8.7 

12.3 

10.0 

12.3 

8.6 

50 

7.8 

11.2 

8.7 

11.2 

7.5 

40 

6.7 

9.9 

7.9 

9.9 

6.6 

30 

5.7 

8.6 

7.0 

8.6 

5.7 

20 

4.5 

7.4 

5.8 

7.6 

4.7 

10 

3.0 

5.4 

4.2 

6.1 

3.2 

5 

1.7 

3.8 

3.0 

5.1 

1.8 

No.  of  ^ 

pupils  | 

1412 

1705 

1699 

1717 

1642 

58 


TABLE  II-A.    MONROE'S  STANDARDIZED  SILENT  READING  TEST.  COMPRE- 
HENSION.   PERCENTILE   SCORES    BASED   OM    MAY   TESTING. 

FORM  1 


GRADE 

PERCENTILE 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

VI 

XII 

95 

20.8 

24.2 

33.8 

38.6 

39.4 

43.9 

51.5 

50.1 

51.8 

58.4 

90 

14.4 

20.0 

26.7 

34.0 

35.7 

40.4 

43.3 

45.0 

42.1 

51.7 

80 

11.2 

16.5 

22.6 

28.3 

30.1 

35.4 

36.3 

39.0 

40.0 

42.5 

70 

8.9 

14.0 

19.4 

24.2 

26.5 

31.6 

31.0 

33.9 

35.9 

40.2 

60 

7.0 

12.2 

17.1 

20.2 

23.6 

27.5 

27.3 

29.8 

32.1 

36.5 

50 

5.2 

10.5 

14.9 

18.8 

21.0 

24.1 

24.0 

25.8 

28.5 

33.3 

40 

4.1 

8.7 

13.2 

16.7 

18.8 

23.6 

20.8 

21.4 

26.0 

30.5 

30 

3.1 

7.0 

11.4 

14.5 

16.8 

19.4 

17.6 

19.0 

23.2 

25.1 

20 

2.0 

5.1 

9.4 

12.0 

14.6 

16.7 

14.3 

16.1 

20.2 

21.7 

10 

1.0 

2.6 

6.2 

9.0 

11.4 

13.1 

10.7 

10.3 

15.3 

16.1 

5 

.5 

1.3 

4.0 

6.1 

9.4 

10.8 

7.4 

8.2 

11.6 

11.3 

Number  of  pupils 

1464 

1805 

1729 

1871 

1270 

1337 

783 

397 

236 

230 

FORM  2 


GRADE 


JPERCENTILE 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

95 

21.0 

27.2 

29.7 

39.6 

43.8 

45.8 

48.6 

52.4 

56.3 

58.9 

90 

17.6 

24.1 

27.2 

36.0 

40.0 

42.9 

41.7 

46.1 

49.7 

51.8 

80 

13.6 

20.3 

24.6 

31.1 

35.4 

38.5 

34.9 

39.1 

42.9 

43.6 

70 

11.0 

17.5 

22.3 

28.1 

32.2 

35.2 

30.8 

34.0 

38.0 

39.7 

60 

9.2 

14.9 

20.0 

25.6 

29.3 

32.6 

27.5 

30.1 

33.1 

35.9 

50 

7.9 

13.4 

17.9 

22.7 

27.0 

29.9 

24.5 

26.7 

29.4 

32.1 

40 

6.4 

12.0 

15.7 

19.7 

24.6 

27.6 

21.5 

23.5 

25.9 

28.4 

30 

5.0 

10.5 

13.5 

16.9 

21.4 

25.3 

18.2 

20.6 

22.8 

24.9 

20 

3.3 

8.5 

11.6 

14.0 

17.9 

21.6 

14.6 

16.7 

19.9 

20.3 

10 

1.7 

6.0 

8.0 

12.2 

14.1 

17.1 

10.2 

12.3 

15.1 

16.1 

5 

.8 

4.2 

6.5 

8.0 

11.3 

14.0 

6.8 

10.0 

11.3 

12.6 

N  imber  of  pupils 

8741 

10625 

10157 

9404 

8791 

7561 

781 

625 

443 

320 

FORM  3 


GRADE 

PERCENTILE 

III 

IV 

V 

VI 

VI 

VII 

95 

22.2 

25.1 

27.7 

41.9 

44.6 

46.0 

90 

19.4 

23.8 

25.6 

37.7 

41.7 

43.6 

80 

15.7 

21.3 

23.6 

31.9 

36.9 

39.9 

70 

13.4 

19.1 

22.2 

27.6 

32.9 

37.0 

60 

11.5 

17.1 

20.6 

24.8 

29.4 

35.3 

50 

9.6 

15.2 

19.0 

22.1 

26.5 

31.1 

40 

8.0 

13.5 

17.3 

19.4 

23.8 

28.3 

30 

6.4 

11.2 

15.3 

16.6 

20.4 

25.5 

20 

4.7 

9.0 

12.8 

13.8 

18.2 

22.1 

10 

2.3 

5.8 

10.1 

11.0 

13.7 

17.5 

5 

1.2 

3.3 

7.1 

8.5 

11.3 

13.9 

Number  of  pupils 

1604 

1680 

1704 

1580 

1513 

1186 

TABLE  II-B.    MONROE'S  STANDARDIZED  SILENT  READING  TEST. 
PERCENTILE  SCORES  BASED  ON  MAY  TESTING 

FORM  1 


RATE 


GRADE 

PERCENTILE 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

95 

98.0 

111.0 

143.5 

145.4 

146.6 

148.9 

136.6 

143.0 

138.3 

152.1 

90 

84.5 

105.9 

126.9 

143.8 

142.7 

146.9 

120.9 

130.1 

130.9 

137.4 

80 

70.7 

81.0 

110.0 

115.5 

120.3 

142.7 

109.5 

120.2 

121.5 

129.4 

70 

60.6 

80.6 

96.4 

103.6 

110.9 

135.6 

100.8 

100.4 

105.0 

122.7 

60 

52.2 

72.8 

87.0 

95.3 

102.0 

115.1 

86.7 

88.5 

92.0 

107.6 

50 

44.5 

65.2 

78.8 

89.0 

95.1 

105.6 

82.6 

84.4 

86.6 

102.7 

40 

38.0 

58.1 

73.0 

73.0 

88.8 

97.2 

78.1 

80.3 

83.1 

88.2 

30 

33.0 

51.7 

65.9 

67.6 

82.8 

91.1 

73.3 

75.6 

79.5 

84.2 

20 

20.6 

44.4 

56.7 

60.2 

66.6 

82.5 

66.3 

70.7 

74.4 

80.2 

10 

10.6 

34.3 

44.6 

49.8 

58.2 

62.3 

55.3 

61.5 

67.9 

69.2 

5 

5.2 

25.0 

34.6 

41.1 

51.5 

53.4 

50.0 

54.9 

58.3 

60.8 

Number  of  pupils 

1464 

1840 

1828 

1869 

1279 

1357 

785 

397 

235 

220 

FORM  2 


GRADE 


rERUENTlLE 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

95 

117.4 

126.7 

128.4 

165.9 

167.2 

168.0 

137.9 

138.7 

140.4 

147.9 

90 

98.5 

122.2 

126.3 

161.7 

164.4 

165.9 

130.4 

132.2 

134.1 

139.2 

80 

78.0 

107.0 

122.1 

147.0 

157.3 

161.8 

123.6 

123.6 

125.8 

130.7 

70 

71.8 

96.9 

114.3 

136.3 

146.0 

154.6 

107.6 

107.2 

109.8 

123.5 

60 

67.0 

90.7 

104.6 

124.3 

137.4 

145.2 

101.5 

103.2 

104.1 

107.5 

50 

62.6 

76.6 

97.2 

114.1 

131.5 

137.4 

87.2 

88.6 

89.0 

102.3 

40 

55.7 

71.9 

91.5 

107.8 

115.8 

131.5 

82.9 

83.8 

84.3 

87.6 

30 

45.5 

67.1 

76.9 

100.8 

109.1 

115.5 

78.1 

79.0 

.79.6 

83.1 

20 

36.8 

62.2 

71.3 

82.7 

101.2 

107.7 

72.0 

74.1 

73.1 

77.5 

10 

28.9 

49.5 

63.1 

72.1 

80.5 

88.1 

62.9 

67.1 

61.9 

69.6 

5 

15.5 

37.8 

55.4 

54.9 

72.2 

79.7 

56.1 

57.2 

54.7 

59.8 

Number  of  pupils 

9739 

10579 

10150 

9853 

8767 

7681 

781 

626 

443 

322 

FORM  3 


GRADE 

PERCENTILE 

III 

IV 

V 

VI 

VII 

VIII 

95 

123.3 

127.0 

128.3 

146.7 

148.3 

148.8 

90 

109.9 

123.9 

126.7 

142.8 

146.2 

147.2 

80 

99.4 

114.7 

123.3 

124.1 

141.9 

143.9 

70 

89.0 

106.6 

119.9 

114.  9 

124.6 

140.5 

60 

84.5 

101.6 

109.6 

107.7 

115.9 

124.0 

50 

80.0 

93.8 

105.6 

101.1 

109.0 

117.3 

40 

72.3 

86.9 

101.6 

94.1 

102.5 

112.2 

30 

55.1 

81.4 

94.2 

86.9 

95.0 

106.0 

20 

46.7 

72.6 

85.7 

79.6 

86.8 

98.3 

10 

42.7 

48.9 

75.6 

69.1 

77.5 

85.2 

5 

22.7 

43.8 

59.6 

59.2 

65.3 

76.5 

Numbe*-  of  pupils 

1608 

1695 

1702 

1579 

1528 

1179 

60 


TABLE  III-A.    CHARTERS'  DIAGNOSTIC  LANGUAGE  TESTS  FOR  GRADES 

III  TO  VIII.    PRONOUNS.    FORM  I.    PERCENTILE  SCORES 

BASED  ON  MARCH  TESTING. 


GRADE 

PERCENTILE 

III 

IV 

V 

VI 

VII 

VIII 

95 

27.9 

27.7 

30.7 

32.2 

35.4 

38.9 

90 

24.8 

24.8 

27.5 

29.7 

33.3 

37.5 

80 

21.3 

21.5 

23.6 

26.9 

30.6 

35.0 

70 

18.5 

19.3 

21.7 

24.7 

28.4 

32.9 

60 

15.8 

16.9 

20.1 

22.9 

26.3 

31.1 

50 

13.6 

15.1 

18.5 

21.4 

24.5 

29.0 

40 

11.7 

13.5 

16.8 

19.7 

22.5 

26.9 

30 

9.9 

11.9 

15.2 

17.9 

20.7 

24.4 

20 

7.8 

10.0 

13.3 

16.0 

18.5 

21.3 

10 

5.1 

7.6 

10.9 

13.2 

15.5 

16.0 

5 

3.3 

5.8 

9.5 

10.6 

13.1 

10.9 

No.  of  pupils 

787 

864 

895 

1344 

1566 

1253 

TABLE  III-B.    CHARTERS'  DIAGNOSTIC  LANGUAGE  TEST  FOR  GRADES 

III  TO  VIII.    VERBS  (FORMERLY  VERBS  A.)    FORM  I.    PER. 

CENTILE  SCORES  BASED  ON  MARCH  TESTING. 


GRADE 


rERCENTILE 

III 

IV 

V 

VI 

VII 

VIII 

95 

29.2 

32.0 

34.4 

37.0 

36.3 

39.4 

90 

25.3 

29.0 

32.2 

34.3 

34.7 

38.4 

80 

20.5 

24.3 

29.5 

31.0 

32.7 

36.8 

70 

17.8 

21.6 

27.4 

28.1 

31.1 

35.5 

60 

15.0 

19.5 

25.4 

26.1 

29.4 

34.2 

50 

12.6 

17.7 

22.6 

24.3 

27.7 

32.8 

40 

10.8 

15.9 

20.7 

22.4 

25.6 

31.2 

30 

8.2 

13.9 

18.6 

20.2 

23.4 

29.6 

20 

6.2 

11.7 

15.3 

17.7 

21.5 

27.2 

10 

3.9 

8.8 

11.5 

13.6 

18.6 

23.4 

5 

2.7 

6.4 

7.4 

11.3 

16.4 

20.8 

No.  of  pupils 

365 

403 

373 

478 

539 

638 

M 


TABLE   III-C.    CHARTERS'    DIAGNOSTIC   LANGUAGE  TEST   FOR   GRADES 

III  TO  VIII.    MISCELLANEOUS  A   (FORMERLY   MISCELLANEOUS) 

FORM  I.    PERCENTILE  SCORES  BASED  ON  MARCH  TESTING 


GRADE 

PERCENTILE 

III 

IV 

V 

VI 

VII 

VIII 

95 

27.9 

23.8 

22.3 

29.7 

31.9 

34.6 

90 

24.1 

18.6 

19.1 

26.6 

28.9 

31.6 

80 

15.9 

15.1 

16.9 

23.0 

25.8 

28.3 

70 

11.5 

12.6 

15.0 

20.6 

21.9 

26.2 

60 

8.7 

10.8 

13.3 

18.6 

19.7 

24.1 

50 

6.7 

9.3 

11.6 

16.5 

18.9 

22.3 

40 

5.7 

7.9 

10.2 

14.6 

17.2 

20.3 

30 

4.6 

6.4 

9.0 

12.7 

15.5 

17.9 

20 

3.3 

5.1 

7.3 

10.8 

13.4 

15.4 

10 

2.0 

3.4 

5.5 

8.5 

10.4 

12.0 

5 

1.4 

2.6 

4.1 

6.5 

7.9 

9.1 

No.  of  pupils 

386 

669 

668 

845 

758 

494 

TABLE   III-D.    CHARTERS'    DIAGNOSTIC   LANGUAGE   TEST   FOR    GRADES 

III  TO  VIII.     MISCELLANEOUS  B  (FORMERLY  VERBS  B).     FORM  I. 

PERCENTILE  SCORES  BASED  ON  MARCH  TESTING 


GRADE 


rERCENTILE 

III 

IV 

V 

VI 

VII 

VIII 

95 

27.5 

31.7 

33.7 

38.7 

39.0 

38.5 

90 

20.2 

29.5 

31.5 

36.4 

37.2 

37.3 

80 

16.7 

25.9 

28.8 

33.5 

34.6 

35.7 

70 

13.3 

22.9 

26.4 

31.4 

32.8 

34.6 

60 

10.3 

20.2 

24.0 

29.4 

31.2 

33.4 

50 

7.9 

17.8 

22.0 

27.3 

29.4 

32.0 

40 

5.0 

14.6 

19.5 

24.7 

27.4 

30.7 

30 

3.7 

11.9 

16.9 

21.7 

25.4 

28.9 

20 

2.5 

9.4 

14.4 

18.0 

21.9 

26.7 

10 

1.3 

6.5 

10.9 

13.9 

18.2 

24.3 

5 

0.7 

3.7 

7.1 

10.2 

15.5 

21.2 

No.  of  pupils 

230 

430 

307 

475 

412 

294 

62 


TABLE   IV.    CHARTER'S   DIAGNOSTIC   LANGUAGE   AND   GRAMMAR   TEST 

FOR  GRADES  VII  AND  VIII.    FORM  I.    PERCENTILE  SCORES  BASED 

ON   APRIL   TESTING 


Pronouns 

Verbs 

Miscellaneous 

PERCENTILE 

GRADE 

GRADE 

GRADE 

VII 

VIII 

VII 

VIII 

VII 

VIII 

95 

27.9 

33.4 

36.4 

34.5 

20.9 

30.6 

90 

23.5 

32.5 

34.1 

31.5 

17.0 

26.4 

80 

17.6 

27.7 

27.4 

26.3 

12.9 

21.7 

70 

13.0 

24.0 

17.6 

21.3 

10.4 

17.0 

60 

10.2 

20.5 

11.8 

16.8 

7.8 

14.4 

50 

8.0 

17.1 

7.8 

14.0 

6.3 

11.9 

40 

6.3 

13.7 

5.0 

10.9 

5.1 

9.5 

30 

4.9 

10.2 

3.5 

8.3 

3.3 

7.2 

20 

3.5 

7.0 

2,3 

5.4 

2.3 

5.1 

10 

2.1 

4.2 

1.1 

3.0 

.9 

3.1 

5 

1.3 

3.0 

.5 

1.9 

.5 

2.2 

No.  of  pupils 

936 

657 

434 

497 

332 

362 

TABLE  V-A.    WILLING 'S  SCALE  FOR  MEASURING  WRITTEN  COMPOSITION, 
STORY  VALUE.    PERCENTILE  SCORES  BASED  ON  MARCH  TESTING 


GRADE 


FERCENTILE 

IV 

V 

VI 

VII 

VIII 

IX 

95 

76.3 

89.9 

93.2 

95.7 

96.1 

95.3 

90 

66.1 

85.5 

88.2 

91.5 

96.0 

90.8 

80 

57.5 

77.7 

81.5 

88.1 

88.6 

87.5 

70 

52.1 

71.3 

76.8 

82.8 

84.6 

84.9 

60 

46.8 

65.0 

72.6 

78.0 

80.5 

82.2 

50 

41.5 

58.7 

68.1 

74.0 

76.6 

79.0 

40 

36.9 

52.8 

63.3 

69.2 

72.9 

73.8 

30 

32.7 

46.6 

58.0 

63.5 

68.7 

68.4 

20 

28.4 

40.2 

51.5 

50.1 

62.2 

62.3 

10 

24.2 

31.5 

43.1 

46.0 

54.7 

53.3 

5 

22.1 

26.0 

37.0 

37.4 

46.9 

43.6 

No.  of  pupils 

320 

579 

705 

692 

572 

129 

63 


TABLE  V-B.    WILLING'S  SCALE  FOR  MEASURING  WRITTEN  COMPOSITION, 

ERRORS  PER  100  WORDS.    PERCENTILE  SCORES  BASED 

ON  MARCH  TESTING 


GRADE 

PERCENTILE 

IV 

V 

VI 

VII 

VIII 

IX 

95 

32.1 

28.8 

18.8 

18.1 

14.8 

11.9 

90 

31.7 

24.9 

16.0 

13.9 

11.9 

10.3 

80 

28.2 

19.4 

11.9 

10.8 

8.8 

7.9 

70 

23.9 

15.6 

9.9 

8.7 

7.4 

6.0 

60 

20.9 

12.5 

8.2 

7.3 

6.1 

5.2 

50 

18.5 

10.7 

6.8 

5.8 

5.2 

4.4 

40 

15.5 

9.3 

5.5 

4.8 

4.4 

3.6 

30 

13.0 

7.3 

4.2 

3.8 

3.6 

2.8 

20 

10.3 

5.3 

3.0 

2.6 

2.5 

1.9 

10 

7.3 

3.5 

1.6 

1.3 

1.2 

.9 

5 

5.4 

2.1 

.7 

.7 

.6 

.5 

No.  of  pupils 

327 

578 

702 

693 

473 

129 

TABLE  VI.    HARLAN'STESTOFINFOR. 

MATION   IN   AMERICAN   HISTORY 

PERCENTILE     SCORES     BASED 

ON    MAY    TESTING 


JTEKIENTILE 

VII 

VIII 

95 

78.8 

95.2 

90 

70.9 

94.1 

80 

56.6 

92.2 

70 

54.0 

81.1 

60 

48.8 

74.9 

50 

43.9 

68.2 

40 

38.8 

56.7 

30 

31.9 

50.9 

20 

27.1 

41.3 

10 

20.1 

31.4 

5 

15.5 

27.7 

Number  of  pupils 

1109 

1691 

GRADE 


64 


TABLE  VII.    HOTZ'S  FIRST  YEAR  ALGEBRA  SCALES,  SERIES  A 
PERCENTILE  SCORES  BASED  ON  MAY  TESTING 


PERCENTILE 

Addition 
and 
Subtraction 

Multipli- 
cation and 
Division 

Problems 

Equations 
and 
Formulas 

Graphs 

GRADE 

GRADE 

GRADE 

GRADE 

GRADE 

IX 

X 

IX 

X 

IX 

X 

IX 

X 

IX 

X 

95 
90 
80 
70 
60 
50 
40 
30 
20 
10 
5 

11.7 
10.8 
9.6 
8.6 

7.7 
6.9 
6.3 
5.7 
4.8 
3.7 
2.9 

10.5 
9.7 
8.9 
8.4 
8.0 
7.3 
6.7 
6.1 
5.5 
4.3 
3.2 

10.4 
9.7 
8.7 
8.1 
7.6 
7.2 
6.6 
6.0 
5.4 
4.6 
4.0 

10.7 
10.0 
9.0 
8.4 
7.8 
7.4 
6.9 
6.2 
5.6 
4.9 
4.2 

10.6 
9.9 
9.0 
8.1 
7.3 
6.4 
5.7 
4.8 
3.8 
2.6 
1.5 

9.3 
7.6 
6.6 
5.9 
5.3 
5.0 

12.3 
11.5 
10.3 
9.3 
8.6 
7.7 

11.0 
10.4 
9.5 
8.8 
8.2 
7.9 

8.0 

7.5 
7.2 
6.8 
6.5 
6.2 

7.5 
6.9 
6.3 
5.8 
5.4 
5.0 

4.1 
3.6 
2.9 

2.2 

6.4 

5.7 

7.0 
6.4 

5.4 
5.0 

4.3 
3.9 
3.3 
2.8 

3.7 

4.3 

3.7 

Number  of  pupils 

561 

390 

570 

388 

566 

394 

478 

385 

121 

413 

TABLE  VIII.    HOLLEY'S  SENTENCE  VOCABULARY  SCALES.    PERCENTILE 
SCORES    BASED    ON     APRIL    TESTING 


GRADE 


rercenrne 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

95 

72.7 

53.5 

45.2 

50.9 

65.5 

63.9 

66.5 

68.5 

75.2 

77.9 

82.3 

90 

68.5 

44.7 

40.0 

47.6 

61.0 

58.5 

62.6 

64.6 

70.0 

75.0 

78.2 

80 

63.8 

32.3 

35.7 

42.4 

54.7 

52.5 

57.4 

58.7 

66.0 

69.6 

73.1 

70 

59.6 

25.7 

31.6 

38.5 

49.2 

48.2 

54.2 

55.5 

61.8 

66.4 

68.8 

60 

57.2 

20.0 

28.2 

35.8 

46.2 

45.1 

50.9 

52.3 

58.7 

63.1 

65.8 

50 

54.8 

16.7 

25.1 

33.0 

42.8 

41.9 

47.8 

49.0 

56.1 

59.9 

62.8 

40 

52.4 

13.4 

22.1 

30.3 

39.5 

38.4 

44.7 

45.8 

53.4 

56.9 

59.7 

30 

50.0 

10.1 

18.7 

27.0 

35.5 

34.3 

41.6 

42.6 

50.8 

53.9 

56.3 

20 

46.1 

6.8 

14.7 

23.6 

31.4 

30.2 

36.8 

38.9 

46.6 

51.0 

52.8 

10 

42.2 

3.4 

10.7 

20.2 

24.9 

20.9 

30.0 

33.9 

41.6 

45.4 

48.3 

5 

40.3 

1.7 

6.0 

13.1 

21.1 

13.4 

22.8 

31.3 

37.4 

42.1 

44.1 

No.  of 

pupils 

117 

406 

520 

465 

450 

1188 

1047 

253 

223 

155 

108 

T.A.ST 


YC  836^ 


UNIVERSITY  OF  CALIFORNIA  UBRARY 

r 


